This research area includes analysis of differential equations, especially those which occur in applications in the natural sciences, such as fluid dynamics, materials science, or mathematical physics. Analysis and Partial Differential Equations also includes topics like calculus of variations, harmonic/wavelet analysis, and classic analysis.

By Patrick De Leenheer SIAM Review, Volume 62, Issue 3, Page 716-726, January 2020. We present an elementary proof of a generalization of Kirchhoff's matrix tree theorem to directed, weighted graphs. The proof...

By Lek-Heng Lim SIAM Review, Volume 62, Issue 3, Page 685-715, January 2020. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian....

By Andrii Mironchenko and Christophe Prieur SIAM Review, Volume 62, Issue 3, Page 529-614, January 2020. In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems....

By Ernesto Estrada, Gissell Estrada-Rodriguez, and Heiko Gimperlein SIAM Review, Volume 62, Issue 3, Page 617-645, January 2020. In a complex system, the interplay between the internal structure of its entities and their interconnection may play a...

By Jed A. Duersch and Ming Gu SIAM Review, Volume 62, Issue 3, Page 661-682, January 2020. Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and...

By Vicky Chuqiao Yang, Daniel M. Abrams, Georgia Kernell, and Adilson E. Motter SIAM Review, Volume 62, Issue 3, Page 646-657, January 2020. Since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 3, Page 683-683, January 2020. This issue of SIAM Review contains two papers in the Education section. The first paper, “Hodge Laplacians on Graphs,”...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 3, Page 615-615, January 2020. In this issue, Research Spotlights features two exciting and topically diverse articles. The authors of the first article...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 3, Page 527-527, January 2020. Andrii Mirochenko and Christophe Prieur are the authors of “Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions,”...

By Volker H. Schulz SIAM Review, Volume 62, Issue 3, Page 729-739, January 2020. These are difficult times, but some circumstances make the work in our Book Reviews section even more difficult. Due...

By The Editors SIAM Review, Volume 62, Issue 3, Page 659-659, January 2020. The SIGEST article in this issue, “Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations,” by Jed A. Duersch...

By Annika Bach, Andrea Braides, and Marco Cicalese SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3600-3665, January 2020. We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence....

By Yong Liu and Juncheng Wei SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3546-3579, January 2020. For each positive integer $n\leq34,$ we construct traveling waves with small speed for the Gross--Pitaevskii equation,...

By Giovanni Di Fratta, Cyrill B. Muratov, Filipp N. Rybakov, and Valeriy V. Slastikov SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3580-3599, January 2020. We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with...

By Guillaume Bal and Benjamin Palacios SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3487-3519, January 2020. Solutions of stationary Fokker--Planck equations in the narrow beam regime are commonly approximated by either ballistic...

By Fei Wang SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3520-3545, January 2020. We consider the three-dimensional Navier--Stokes equations in the upper half space ${\mathbb H^3_+}$ with periodic boundary...

By Patrick De Leenheer SIAM Review, Volume 62, Issue 3, Page 716-726, January 2020. We present an elementary proof of a generalization of Kirchhoff's matrix tree theorem to directed, weighted graphs. The proof...

By Lek-Heng Lim SIAM Review, Volume 62, Issue 3, Page 685-715, January 2020. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian....

By Andrii Mironchenko and Christophe Prieur SIAM Review, Volume 62, Issue 3, Page 529-614, January 2020. In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems....

By Ernesto Estrada, Gissell Estrada-Rodriguez, and Heiko Gimperlein SIAM Review, Volume 62, Issue 3, Page 617-645, January 2020. In a complex system, the interplay between the internal structure of its entities and their interconnection may play a...

By Jed A. Duersch and Ming Gu SIAM Review, Volume 62, Issue 3, Page 661-682, January 2020. Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and...

By Vicky Chuqiao Yang, Daniel M. Abrams, Georgia Kernell, and Adilson E. Motter SIAM Review, Volume 62, Issue 3, Page 646-657, January 2020. Since the 1960s, Democrats and Republicans in the U.S. Congress have taken increasingly polarized positions, while the public's policy...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 3, Page 683-683, January 2020. This issue of SIAM Review contains two papers in the Education section. The first paper, “Hodge Laplacians on Graphs,”...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 3, Page 615-615, January 2020. In this issue, Research Spotlights features two exciting and topically diverse articles. The authors of the first article...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 3, Page 527-527, January 2020. Andrii Mirochenko and Christophe Prieur are the authors of “Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions,”...

By Volker H. Schulz SIAM Review, Volume 62, Issue 3, Page 729-739, January 2020. These are difficult times, but some circumstances make the work in our Book Reviews section even more difficult. Due...

By The Editors SIAM Review, Volume 62, Issue 3, Page 659-659, January 2020. The SIGEST article in this issue, “Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations,” by Jed A. Duersch...

By Annika Bach, Andrea Braides, and Marco Cicalese SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3600-3665, January 2020. We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence....

By Yong Liu and Juncheng Wei SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3546-3579, January 2020. For each positive integer $n\leq34,$ we construct traveling waves with small speed for the Gross--Pitaevskii equation,...

By Giovanni Di Fratta, Cyrill B. Muratov, Filipp N. Rybakov, and Valeriy V. Slastikov SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3580-3599, January 2020. We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with...

By Guillaume Bal and Benjamin Palacios SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3487-3519, January 2020. Solutions of stationary Fokker--Planck equations in the narrow beam regime are commonly approximated by either ballistic...

By Fei Wang SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3520-3545, January 2020. We consider the three-dimensional Navier--Stokes equations in the upper half space ${\mathbb H^3_+}$ with periodic boundary...

By Steven Schochet and Xin Xu SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3444-3462, January 2020. A uniform existence theorem is proven for quasilinear symmetric hyperbolic systems containing two small parameters tending...

By Vladimir Yu. Protasov SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3463-3486, January 2020. We study the surface regularity of compact sets $G \subset {\mathbb R}^n$ which is equal to...

By E. P. Balanzario and E. I. Kaikina SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3376-3396, January 2020. We consider the stochastic nonlinear Landau--Ginzburg equations on the half-line with Dirichlet white-noise boundary conditions. We...

By Hirokazu Saito, Yoshihiro Shibata, and Xin Zhang SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3397-3443, January 2020. In this paper, we establish some local and global solutions for the two-phase incompressible inhomogeneous flows...

By Haigang Li SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3350-3375, January 2020. In the perfect conductivity problem of composite material, the electric field concentrates in a narrow region...

By Matthew Novack SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3301-3349, January 2020. We show that weak solutions to the 3 dimensional quasi-geostrophic system in the class $C^\zeta_{t,x}$ for...

By Adolfo Arroyo-Rabasa and Johannes Diermeier SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3252-3300, January 2020. This paper is devoted to the construction of generalized multiscale Young measures, which are the extension...

By Adam Bobrowski SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3222-3251, January 2020. Motivated by models of signaling pathways in B-lymphocytes, which have extremely large nuclei, we study the...

By Bing Li, Masahito Ohta, Yifei Wu, and Jun Xue SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3192-3221, January 2020. In this work, we consider the generalized Boussinesq equation $\partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\ (t,x)\in\mathbb{R}\times \mathbb{R}$, with $0

By Fenfen Wang and Rafael de la Llave SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3149-3191, January 2020. We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs),...

By Hartmut Pecher SIAM Journal on Mathematical Analysis, Volume 52, Issue 4, Page 3131-3148, January 2020. The Cauchy problem for the Yang--Mills system in three space dimensions with data in Fourier--Lebesgue spaces...

By Dingqun Deng SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3093-3113, January 2020. In this paper, we find that the linearized collision operator $L$ of the non-cutoff Boltzmann equation...

By Peter Constantin, Theodore D. Drivas, and Roman Shvydkoy SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3073-3092, January 2020. We develop a method of obtaining a hierarchy of new higher-order entropies in the context of...

By Yan Shu SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3052-3072, January 2020. We study the properties of the Hopf--Lax formula restricted to convex functions and provide a characterization...

By Helge Kristian Jenssen and Johanna Ridder SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3114-3130, January 2020. We show that the Kružkov solution of the Cauchy problem for a scalar conservation law in...

By Amir Sagiv and Stefan Steinerberger SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3039-3051, January 2020. Let $f: (0,1)^d \rightarrow \mathbb{R}$ be a continuous function with zero mean and interpret $f_{+}...

By Patrick Ciarlet SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3004-3038, January 2020. In bounded domains, the regularity of the solutions to boundary value problems depends on the geometry,...

By Achenef Tesfahun SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2969-3003, January 2020. We prove that the initial value problem for the Dirac equation $(-i\gamma^\mu \partial_\mu + m) \psi=...

By Carlo Marcati and Christoph Schwab SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2945-2968, January 2020. In a plane polygon $P$ with straight sides, we prove analytic regularity of the Leray--Hopf solution...

By Cyril Imbert, Clément Mouhot, and Luis Silvestre SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2930-2944, January 2020. The study of positivity of solutions to the Boltzmann equation goes back to [T. Carleman, Acta...

By Jörg Weber SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2895-2929, January 2020. The time evolution of a collisionless plasma is modeled by the relativistic Vlasov--Maxwell system which couples...

By Jean-Claude Saut and Li Xu SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2803-2848, January 2020. This paper is concerned with the one-dimensional version of a specific member of the (abcd) family...

By Yann Brenier and Dmitry Vorotnikov SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2849-2873, January 2020. We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired...

By Simone Dovetta, Marco Ghimenti, Anna Maria Micheletti, and Angela Pistoia SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2874-2894, January 2020. We consider the nonlinear Schrödinger equation with focusing power-type nonlinearity on compact graphs with at least...

By Peter Gladbach, Eva Kopfer, and Jan Maas SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2759-2802, January 2020. We consider dynamical transport metrics for probability measures on discretizations of a bounded convex domain in...

By Carsten Hartmann, Lara Neureither, and Upanshu Sharma SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2689-2733, January 2020. This work is concerned with model reduction of stochastic differential equations and builds on the idea...

By Ru-Yu Lai and Qin Li SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2734-2758, January 2020. We consider the inverse problem for the general transport equation with external field, source term, and...

By Ru-Yu Lai, Yi-Hsuan Lin, and Angkana Rüland SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2655-2688, January 2020. In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with...

By Helmut Abels and Julia Butz SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2592-2623, January 2020. We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to...

By Danielle Hilhorst, Hiroshi Matano, Thanh Nam Nguyen, and Hendrik Weber SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2624-2654, January 2020. In this paper, we study the generation of interface for the solution of the mass conserved...

By Barbara Niethammer and Richard Schubert SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2561-2591, January 2020. We prove a local variant of Einstein's formula for the effective viscosity of dilute suspensions, that...

By Sara Daneri and Eris Runa SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2531-2560, January 2020. In this paper we study pattern formation for a physical local/nonlocal interaction functional where the local...

By Sam G. Krupa and Alexis F. Vasseur SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2491-2530, January 2020. In this paper, we show uniqueness and stability for the piecewise-smooth solutions, with a single discontinuity,...

By George C. Hsiao and Tonatiuh Sánchez-Vizuet SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2463-2490, January 2020. This paper is concerned with the application of time-domain boundary integral methods to a nonstationary boundary...

By Weiwei Ding and Hiroshi Matano SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2411-2462, January 2020. This paper is concerned with the Cauchy problem $u_{t}=u_{xx}+f(t,u),x\in \mathbb{R} ,t>0$ with initial function $u(0,\cdot)=u_0 (\cdot)\in...

By Grzegorz Karch, Moritz Kassmann, and Miłosz Krupski SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2383-2410, January 2020. We study the Cauchy problem for nonlinear, nonlocal operators that may be degenerate. Our general framework...

By Gi-Chan Bae and Seok-Bae Yun SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2313-2352, January 2020. In this paper, we consider the existence and asymptotic behavior of the fermionic quantum BGK model,...

By E. Dinvay, S. Selberg, and A. Tesfahun SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2353-2382, January 2020. We regard the Cauchy problem for a particular Whitham--Boussinesq system modeling surface waves of an inviscid...

By Ling Guo, Akil Narayan, and Tao Zhou SIAM Review, Volume 62, Issue 2, Page 483-508, January 2020. Polynomial approximations constructed using a least-squares approach form a ubiquitous technique in numerical computation. One of the simplest ways...

By Lloyd N. Trefethen SIAM Review, Volume 62, Issue 2, Page 439-462, January 2020. Boundary-value problems involving the linear differential equation $\varepsilon y'' - x y' + y = 0$ have surprising properties...

By Yair Carmon and John C. Duchi SIAM Review, Volume 62, Issue 2, Page 395-436, January 2020. We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these...

By Anne Greenbaum, Ren-Cang Li, and Michael L. Overton SIAM Review, Volume 62, Issue 2, Page 463-482, January 2020. We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general...

By Philipp Grohs, Sarah Koppensteiner, and Martin Rathmair SIAM Review, Volume 62, Issue 2, Page 301-350, January 2020. The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier...

By Michael T. Schaub, Austin R. Benson, Paul Horn, Gabor Lippner, and Ali Jadbabaie SIAM Review, Volume 62, Issue 2, Page 353-391, January 2020. Using graphs to model pairwise relationships between entities is a ubiquitous framework for studying complex systems and data. Simplicial...

By Volker H. Schulz SIAM Review, Volume 62, Issue 2, Page 511-526, January 2020. I am writing these lines in April 2020 while science is in lockdown mode globally. They will be published...

By The Editors SIAM Review, Volume 62, Issue 2, Page 393-393, January 2020. The SIGEST article in this issue, “First-Order Methods for Nonconvex Quadratic Minimization,” by Yair Carmon and John C. Duchi,...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 2, Page 351-351, January 2020. The current issue of SIAM Review features the Research Spotlights article “Random Walks on Simplicial Complexes and the Normalized...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 2, Page 437-438, January 2020. The Education section of SIAM Review presents three papers in this issue. In the first paper Lloyd N. Trefethen...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 2, Page 299-299, January 2020. In a previous issue of SIAM Review, I started my introduction to the Survey and Review section by saying...

By Arnaud Ducrot and Alexandre Genadot SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2275-2312, January 2020. We study the asymptotic behavior of solutions of a class of linear nonlocal measure valued differential...

By Michael Röckner, Bo Wu, Rongchan Zhu, and Xiangchan Zhu SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2237-2274, January 2020. In this paper, we prove the existence of martingale solutions to the stochastic heat equation taking...

By Juan Casado-Díaz, Manuel Luna-Laynez, and Francisco J. Suárez-Grau SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2201-2236, January 2020. In order to study the asymptotic behavior of a fluid in a domain of small thickness...

By Marcel Braukhoff, Xiuqing Chen, and Ansgar Jüngel SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2198-2200, January 2020. We correct the proof of Proposition 2.1 in the paper [S. Hittmeir and A. Jüngel, SIAM...

By Pierre-Etienne Druet and Ansgar Jüngel SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2179-2197, January 2020. The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is...

By Elisa Francini, Giovanni Franzina, and Sergio Vessella SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2134-2157, January 2020. We discuss the well-posedness of the “transient eddy current" magneto-quasi-static approximation of Maxwell's initial value problem...

By Stanley Snelson SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2081-2097, January 2020. We consider weak solutions of the spatially inhomogeneous Landau equation with hard potentials ($\gamma \in (0,1]$),...

By Tau Shean Lim, Yulong Lu, and James H. Nolen SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2098-2133, January 2020. We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this...

By Vu Hoang and Maria Radosz SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2158-2178, January 2020. We investigate a system of nonlocal transport equations in one spatial dimension. The system can be...

By Michael Winkler SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2041-2080, January 2020. The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes equations through transport and buoyancy....

By Seung-Yeal Ha, Shi Jin, and Jinwook Jung SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2000-2040, January 2020. Synchronization phenomena are ubiquitous in strongly correlated oscillatory systems, and the Kuramoto model serves as a...

By Lukas Emmert, Rupert L. Frank, and Tobias König SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1980-1999, January 2020. We consider the liquid drop model for nuclei interacting with a neutralizing homogeneous background of electrons....

By Senping Luo, Xiaofeng Ren, and Juncheng Wei SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1903-1942, January 2020. A two species interacting system motivated by the density functional theory for triblock copolymers contains a...

By Zhenjie Ren and Mauro Rosestolato SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1943-1979, January 2020. We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a...

By Misha Perepelitsa SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1864-1883, January 2020. We consider a class of the first order hyperbolic systems of PDEs that can be written...

By Xiaoping Zhai, Yongsheng Li, and Fujun Zhou SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1806-1843, January 2020. This paper is devoted to the global large solutions to the 3 dimensional compressible Navier--Stokes equations...

By Kaïs Ammari and Faouzi Triki SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1884-1902, January 2020. In the paper we consider the linear inverse problem that consists in recovering the...

By Robert Axel Neiss SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1844-1863, January 2020. In this paper, we discuss a general approach to finding periodic solutions bifurcating from equilibrium points...

By Youjun Deng, Hongjie Li, and Hongyu Liu SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1786-1805, January 2020. This paper is concerned with the analysis of surface polariton resonance for nanoparticles in linear elasticity....

By Matthew Rosenzweig SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1690-1728, January 2020. In this paper, we give a rigorous justification of the point vortex approximation to the family...

By Hind Al Baba, Christian Klingenberg, Ondřej Kreml, Václav Mácha, and Simon Markfelder SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1729-1760, January 2020. The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation...

By Jan Březina, Eduard Feireisl, and Antonín Novotný SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1761-1785, January 2020. We identify a large class of objects---dissipative measure-valued (DMV) solutions to the Navier--Stokes--Fourier system---in which the...

By Georges Griso, Julia Orlik, and Stephan Wackerle SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1639-1689, January 2020. The paper is dedicated to the asymptotic investigation of textiles as an elasticity problem on beam...

By Seung-Yeal Ha, Woojoo Shim, and Yinglong Zhang SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1591-1638, January 2020. In this paper, we study a macroscopic description on the ensemble of Kuramoto oscillators with finite...

By Mauro Garavello and Francesca Marcellini SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1567-1590, January 2020. This paper considers a system of two conservation laws with a Lipschitz continuous flow and deals...

By Weimin Han SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1549-1566, January 2020. This paper is devoted to an analysis of singular perturbations of inequality problems. For a...

By Shifeng Geng, Yanping Lin, and Ming Mei SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1463-1488, January 2020. In this paper, we are concerned with the system of Euler equations with time-dependent damping like...

By Verena Bögelein, Bernard Dacorogna, Frank Duzaar, Paolo Marcellini, and Christoph Scheven SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1489-1525, January 2020. In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus...

By Marco Morandotti and Francesco Solombrino SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1427-1462, January 2020. The mean-field analysis of a multipopulation agent-based model is performed. The model couples a particle dynamics...

By William Rundell and Zhidong Zhang SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1526-1548, January 2020. We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for the nonhomogeneous heat equation in $\Omega\times...

By C. H. S. Hamster and H. J. Hupkes SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1386-1426, January 2020. We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show...

By Ming Chen, Zhilei Liang, Dehua Wang, and Runzhang Xu SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1363-1385, January 2020. We study the energy balance for the weak solutions of the three-dimensional compressible Navier--Stokes equations in...

By Ahmet Arifoski and Petr Siegl SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1343-1362, January 2020. We analyze pseudospectra of the generator of the damped wave equation with unbounded damping. We show...

By Gigliola Staffilani and Bobby Wilson SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1318-1342, January 2020. A characteristic of the defocusing cubic nonlinear Schrödinger equation (NLSE), when defined so that the space...

By Hongjie Dong and Kunrui Wang SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1290-1309, January 2020. We establish several boundary $\varepsilon$-regularity criteria for suitable weak solutions to the three-dimensional incompressible Navier--Stokes equations...

By Evgeniy Y. Panov SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1310-1317, January 2020. Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional...

By Jiří Minarčík and Michal Beneš SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1221-1231, January 2020. Space curve motion describes dynamics of material defects or interfaces and can be found in image...

By Jan Blechta, Josef Málek, and K. R. Rajagopal SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1232-1289, January 2020. In the first part of the paper we provide a new classification of incompressible fluids characterized...

By Wenjia Jing SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1192-1220, January 2020. We revisit the periodic homogenization of Dirichlet problems for the Laplace operator in perforated domains and...

By Jianfeng Lu, Alexander B. Watson, and Michael I. Weinstein SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1115-1145, January 2020. We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying “mass” term....

By Hyunseok Kim and Tai-Peng Tsai SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1146-1191, January 2020. We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a...

By Gui-Qiang Chen, Mikhail Feldman, Jingchen Hu, and Wei Xiang SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1096-1114, January 2020. We are concerned with the suitability of the main models of compressible fluid dynamics for the...

By Tao Tao, Wendong Wang, and Zhifei Zhang SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1040-1095, January 2020. In this paper, we consider the zero-viscosity limit of the Navier--Stokes equations in a half...

By Jerry L. Bona and Jonatan Lenells SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1009-1039, January 2020. The work presented here emanates from questions arising from experimental observations of the propagation of surface...

By Ya-Guang Wang and Shi-Yong Zhu SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 954-966, January 2020. In this paper, we study the occurrence of a back-flow point of the two-dimensional unsteady Prandtl...

By Kazuhiro Ishige, Nobuhito Miyake, and Shinya Okabe SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 927-953, January 2020. Let $u$ be a solution to the Cauchy problem for a fourth-order nonlinear parabolic equation $\partial_t...

By M. Sprengel, G. Ciaramella, and A. Borzì SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 1006-1008, January 2020. Our paper in SIAM J. Math. Anal., 49 (2017), pp. 1681--1704, contains wrong estimates concerning the...

By Atsushi Kawamoto and Manabu Machida SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 967-1005, January 2020. We consider inverse problems for the first- and half-order time-fractional equation. We establish the stability estimates...

By Jaywan Chung, Yong-Jung Kim, Ohsang Kwon, and Xingbin Pan SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 894-926, January 2020. The super- and subsoltuion theory is developed when the nonlinear reaction function is discontinuous at stable...

By S. N. Chandler-Wilde, E. A. Spence, A. Gibbs, and V. P. Smyshlyaev SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 845-893, January 2020. This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed...

By Graziano Crasta and Ilaria Fragalà SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 821-844, January 2020. We study the interior Bernoulli free boundary problem for the infinity Laplacian. Our results cover the...

By Oleg Yu. Imanuvilov and Masahiro Yamamoto SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 718-791, January 2020. We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove...

By V. Duchêne and L. M. Rodrigues SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 792-820, January 2020. We prove the large-time asymptotic orbital stability of strictly entropic Riemann shock solutions of first-order scalar...

By Volker H. Schulz SIAM Review, Volume 62, Issue 1, Page 283-297, January 2020. The frame for the Book Reviews section this time is formed by the books of two very well known...

By The Editors SIAM Review, Volume 62, Issue 1, Page 197-197, January 2020. The SIGEST article in this issue, “Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal...

By Misha E. Kilmer SIAM Review, Volume 62, Issue 1, Page 131-131, January 2020. Tensors, or multiway arrays, are often used for storage of high-dimensional data. In order to have compression, completion,...

By J. M. Sanz-Serna SIAM Review, Volume 62, Issue 1, Page 1-1, January 2020. Bernard Brogliato and Aneel Tanwani are the authors of “Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness,...

By Darinka Dentcheva SIAM Review, Volume 62, Issue 1, Page 229-230, January 2020. The Education section of SIAM Review presents three papers in this issue. In the first paper Robert M. Corless...

By Guillaume Carlier and Maxime Laborde SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 709-717, January 2020. We develop an elementary and self-contained differential approach, in an $L^{\infty}$ setting, for well-posedness (existence, uniqueness,...

By Matteo Novaga and Paola Pozzi SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 682-708, January 2020. We consider a second order gradient flow of the p-elastic energy for a planar theta-network of...

By Hao Jia SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 623-652, January 2020. We give an alternative proof of sharp decay rates and the linear inviscid damping near monotone...

By Tokinaga and Piotr Rybka SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 653-681, January 2020. We study a fractional diffusion problem in the divergence form in one space dimension. We define...

By Dorian Le Peutrec and Boris Nectoux SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 581-604, January 2020. Let $f: \mathbb R^{d} \to \mathbb R$ be a smooth function, and let $(X_t)_{t\ge 0}$ be...

By Dario Feliciangeli and Robert Seiringer SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 605-622, January 2020. We consider the Pekar functional on a ball in $\mathbb{R}^3$. We prove uniqueness of minimizers, and...

By Cătălin I. Cârstea, Tu Nguyen, and Jenn-Nan Wang SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 570-580, January 2020. The aim of this paper is twofold. First, we derive quantitative uniqueness estimates in...

By Xiaochuan Tian and Qiang Du SIAM Review, Volume 62, Issue 1, Page 199-227, January 2020. Many problems in nature, being characterized by a parameter, are of interest both with a fixed parameter value...

By Bernard Brogliato and Aneel Tanwani SIAM Review, Volume 62, Issue 1, Page 3-129, January 2020. This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations is...

By David Hong, Tamara G. Kolda, and Jed A. Duersch SIAM Review, Volume 62, Issue 1, Page 133-163, January 2020. Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor...

By Tracy L. Stepien, Eric J. Kostelich, and Yang Kuang SIAM Review, Volume 62, Issue 1, Page 244-263, January 2020. Most undergraduates have limited experience with mathematical modeling. In an effort to respond to various initiatives, such as the...

By Antônio Francisco Neto SIAM Review, Volume 62, Issue 1, Page 264-280, January 2020. In this work we introduce a new operator based approach to matrix analysis. Our main technical tool comprises an...

By Nawaf Bou-Rabee and Miranda C. Holmes-Cerfon SIAM Review, Volume 62, Issue 1, Page 164-195, January 2020. Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the...

By Robert M. Corless and Leili Rafiee Sevyeri SIAM Review, Volume 62, Issue 1, Page 231-243, January 2020. We look at two classical examples in the theory of numerical analysis, namely, the Runge example for interpolation and...

By Lyle Noakes and Luchezar Stoyanov SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 471-480, January 2020. It was proved in [L. Noakes and L. Stoyanov, Proc. Amer. Math. Soc., 143 (2015),...

By Zhewen Feng, Min-Chun Hong, and Yu Mei SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 481-523, January 2020. We establish the local well-posedness of the general Ericksen-Leslie system in liquid crystals with the initial...

By Radu Ignat, Matthias Kurzke, and Xavier Lamy SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 524-542, January 2020. For varepsilon>0, let u_varepsilon:Omega to R^2 be a solution of the Ginzburg-Landau system -Delta u_varepsilon=\frac1varepsilon^2 u_varepsilon...

By Gergö Nemes and Adri B. Olde Daalhuis SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 437-470, January 2020. Surprisingly, apart from some special cases, simple asymptotic expansions for the associated Legendre functions P_\nu ^\mu...

By Messoud A. Efendiev, Mitsuharu Otani, and Hermann J. Eberl SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 543-569, January 2020. The model that we investigate here is motivated by the mitochondrial swelling process controlled by calcium...

By Bastian Harrach and Yi-Hsuan Lin SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 402-436, January 2020. In this work, we use monotonicity-based methods for the fractional Schrödinger equation with general potentials q...

By Aymeric Baradat SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 370-401, January 2020. In [An Entropic Interpolation Problem for Incompressible Viscid Fluids, preprint, arXiv:1704.02126, 2017] Arnaudon et al. introduced...

By Harald Garcke and Patrik Knopf SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 340-369, January 2020. The Cahn--Hilliard equation is the most common model to describe phase separation processes of a mixture...

By Edoardo Bocchi SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 306-339, January 2020. The floating structure problem describes the interaction between surface water waves and a floating body, generally...

By Mathew A. Johnson and Wesley R. Perkins SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 277-305, January 2020. In this paper, we are interested in studying the modulational dynamics of interfacial waves rising buoyantly...

By Maria Colombo and Luigi De Rosa SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 221-238, January 2020. In this work we investigate some regularization properties of the incompressible Euler equations and of the...

By Florian List, Kundan Kumar, Iuliu Sorin Pop, and Florin Adrian Radu SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 239-276, January 2020. In this work, we consider a mathematical model for flow in an unsaturated porous medium containing...

By Yuki Kaneko, Hiroshi Matsuzawa, and Yoshio Yamada SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 65-103, January 2020. We will study a free boundary problem of nonlinear diffusion equation $u_t=u_{xx}+f(u),t>0, 0

By Yannis Angelopoulos, Rowan Killip, and Monica Visan SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 135-163, January 2020. We consider discrete analogues of two well-known open problems regarding invariant measures for dispersive PDE, namely,...

By Henrik Garde, Nuutti Hyvönen, and Topi Kuutela SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 197-220, January 2020. This work considers properties of the logarithm of the Neumann-to-Dirichlet boundary map for the conductivity equation...

By Jun Geng and Jinping Zhuge SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 104-134, January 2020. In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating...

By Laurent Lafleche SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 164-196, January 2020. This article studies a Fokker--Planck type equation of fractional diffusion with conservative drift $\partial_tf = \Delta^\frac{\alpha}{2}...

By Ayman Moussa SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 42-64, January 2020. This paper solves partially a question suggested by Fontbona and Méléard. The issue is to obtain...

By Bernard Deconinck and Jeremy Upsal SIAM Journal on Mathematical Analysis, Volume 52, Issue 1, Page 1-41, January 2020. We examine the stability of the elliptic solutions of the focusing nonlinear Schrödinger equation (NLS) with...

Update 7/14/20: Today, the Trump Administration rescinded these proposed rules on foreign students studying online, returning to the previous status quo. Thank you to all of the SIAM members who ...

We may not be able to meet in Toronto for this year’s Joint SIAM/CAIMS Annual Meeting (AN20) , but that doesn’t mean we can’t hold the meeting! SIAM and CAIMS are pivoting to virtual with a ...

It's National Volunteer Week! This occasion is an opportunity to celebrate the dedicated individuals who offer their time in exchange for nothing more than making SIAM (and the world) a better ...

Mathematics and statistics play a vital part in everyday life. Mathematical and statistical techniques are used to help solve real-world problems, focusing on topics such as disease spread, ...

Established in 2011, the prize honors Gábor Szegö, a foremost mathematical analyst. It is awarded to one individual in their early career for outstanding research contributions in the area of orthogonal polynomials and special functions, as evidenced in publication in peer-reviewed journals.

This prize was created in 2013 to emphasize George Pólya’s legacy of communicating mathematics effectively. It joins two long-standing Pólya prizes SIAM has awarded in combinatorics and other fields beginning in 1969.

The prize was established in 1995, and named in honor of Germund Dahlquist for his early contributions to the theory of numerical analysis as applied to differential equations. It is awarded for original contributions to fields associated with his work.

Established in 2005, the paper is awarded to the author or authors of the most outstanding paper, as determined by the selection committee, on a topic in partial differential equations.

Established in 2019, the prize is awarded every two years to an early career researcher for recent contributions in the field of partial differential equations.

Established by Idalia Reid in honor of her husband W. T. Reid and first awarded in 1994, the W. T. and Idalia Reid Prize in Mathematics is awarded annually in the broadly-defined areas of differential equations and control theory.

This joint prize was established in 2002 to honor Sonia Kovalevsky and her work on the theory of differential equations. It is awarded to anyone in the scientific or engineering community whose work highlights the achievements of women in applied and computational mathematics. Nominations can be submitted via the AWM website.

The Pioneer Prize is awarded every four years at the International Council for Industrial and Applied Mathematics (ICIAM) Congress to one individual for pioneering work introducing applied mathematical methods and scientific computing techniques to an industrial problem area or a new scientific field of applications. Nominations can be submitted via the ICIAM website.

Established in 1967, the prize honors George David Birkhoff (1884-1944), who served as the American Mathematical Society (AMS) President during 1925-1926. The prize is awarded every three years by SIAM and AMS for an outstanding contribution to applied mathematics. Nominations can be submitted via the AMS website.

Through the generosity and inspiration of Gerald and Judith Porter, the Mathematical Association of America (MAA), American Mathematical Society (AMS), and SIAM offer this annual lecture at the Joint Mathematics Meetings. The lecture, first awarded in 2010, is given on a mathematical topic accessible to the broader community.

Named in honor of I. E. Block, a co-founder and the first managing director of SIAM, this lecture is open to the public at the SIAM Annual Meeting. It is intended to encourage public appreciation of applied mathematics and computational science by reaching out to the local community.

Established in 1959, the prize honors John von Neumann, a founder of modern computing. The prize is awarded annually for distinguished contributions to applied mathematics and for the effective communication of these ideas to the community.

The JPBM Communications Award is given annually to reward and encourage communicators who, on a sustained basis, bring mathematical ideas and information to non-mathematical audiences. The prize may be awarded in two categories: For Public Outreach and For Expository and Popular Books. Nominations can be submitted via the AMS website.

The prize was established in 1986 in memory of Richard C. DiPrima, who served SIAM for many years and in 1979–1980 as SIAM President. It aims to recognize an early career researcher in applied mathematics and is based on the doctoral dissertation.

The prize recognizes students for outstanding solutions to real world math problems. It is awarded to two of the teams judged "Outstanding" in the Mathematical Contest in Modeling (MCM) administered annually by the Consortium for Mathematics and Its Applications (COMAP). Registration is accepted via the COMAP website.

The SIAM Outstanding Paper Prizes bring attention to papers published in SIAM journals. Three awards are made each year to the authors of papers deemed by SIAM journal editors-in-chief worthy of particular attention.

The prize, established in 1985 and originally intended to be awarded periodically, is now awarded annually for contributions to the advancement of applied mathematics on the national or international level.

The SIAM Student Paper Prize is awarded annually to the student author(s) of the most outstanding paper(s) accepted by SIAM journals within the three years preceding the nomination deadline. Starting with the 2018 award, the focus of the prize is to recognize outstanding scholarship by students in SIAM journals.

This prize was established in 1968 to commemorate Theodore von Kármán and his work in aerodynamics. It is awarded every five years for a notable application of mathematics to mechanics or engineering in the five to ten years preceding the award.

This activity group fosters activity in the analysis of partial differential equations and enhances communication between analysts, computational scientists and the broad partial differential equations community. Its goals are to provide a forum where theoretical and applied researchers in the area can meet, to be an intellectual home for researchers in the analysis of partial differential equations, to increase conference activity in partial differential equations, and to enhance connections between SIAM and the mathematics community.

This activity group promotes basic research in orthogonal polynomials and special functions; furthers the application of this subject in other parts of mathematics, and in science and industry; and encourages and supports the exchange of information, ideas, and techniques between workers in this field and other mathematicians and scientists.

SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods.

Multiscale Modeling & Simulation
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SIAM J. on Imaging Sciences
SIAM J. on Mathematical Analysis
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SIAM J. on Numerical Analysis
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General Opportunities

We know it can be overwhelming to keep track of career opportunities that may be relevant to you as a member of the SIAM community. So, we’ve compiled lists of some of our favorite fellowship, internship, and research opportunities. Check ‘em out!

Fellowships

Looking for financial support to further your research? Fellowships often provide funding plus experiential learning opportunities to young researchers. Learn more about fellowship opportunities.

Internships allow you to network and forge connections for future job possibilities, while also exploring possible areas of interest. Look at this list of companies who offer valuable opportunities.

Our community is founded on igniting groundbreaking developments in applied math and computational science. Take a deeper dive into your area of study with one of these opportunities.