Thursday, May 13

Boundary Value Problems for Degenerate Elliptic Equations

(Invited Minisymposium)

10:45 AM-12:45 PM
Room: Atlanta 3

Degenerate elliptic equations arise in a number of continuum problems. Perhaps the best known is the porous medium equation, representing flow in a medium whose diffusivity depends on saturations. The medium may be isotropic or anisotropic; in either case, free boundary problems occur. Recent work on self-similar solutions of multidimensional conservation laws provides another source of such problems: the degeneracy is typically anisotropic, and mathematical results are just now being developed. The speakers in this minisymposium will discuss proved existence of solutions that change sign for a quasilinear model problem, positive solutions to an anisotropic problem, results on conservation law models and their application to weak shock reflection and the von Neumann paradox, and regularity results for a linear anisotropically degenerate equation.

Organizer: Barbara L. Keyfitz
University of Houston

10:45-11:10 Sign-Changing Solutions to Singular Second-Order Boundary Value
P. J. McKenna, University of Connecticut, Storrs
11:15-11:40 Positive Solution to Anisotropic Quasilinear Elliptic Equations
Y .S. Choi and E. H. Kim, University of Connecticut, Storrs
11:45-12:10 On a Degenerate Elliptic Equation Arising in Weak Shock Reflection
Suncica Canic, University of Houston
12:15-12:40 The Regularity of a Singular Equation
Yi Li and Lihe Wang, University of Iowa

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LMH, 1/19/99, MMD, 1/26/99