## Wednesday July 27/4:30

MS34/Harbor 3

# Conservation Laws in Two Dimensions

This minisymposium focuses on two-dimensional wave structures which arise in various applications such as transonic flows, nonlinear acoustics, and nonlinear geometrical optics. In spite of the extensive experimental and numerical studies in this field, not very much is known on a theoretical level. There are open questions concerning the internal structure of higher dimensional elementary waves, bifurcation criteria for two-dimensional elementary waves, and the general existence theory for conservation laws in two dimensions. The speakers in this minisymposium will report on new advances in these areas. The methods are based on the bifurcation diagrams of the shock polars, potential theory and matches asymptotic expansions. In problems like transonic flow, a general existence theory relies on a correct choice of function spaces which reflect the potential singularities in a solution caused by the change in type. A new efficient numerical method for weak shock reflection phenomenon will also be presented.
**Organizer: Suncica Canic
Iowa State University**
*4:30:* ** Potential Theory for Regular and Mach Reflection of a Shock at a Wedge**
Cathleen S. Morawetz, Courant Institute of Mathematical Sciences, New York University
*5:00:*** Weak Mach Reflection in Two-Dimensional Riemann Problems**
Leroy F. Henderson, (retired), State University of New York, Stony Brook, and Sydney, Australia
*5:30:* **Focusing, Diffraction and Reflection of Weak Shock Waves**
*Esteban G. Tabak*, Princeton University; and Ruben R. Rosales, Massachusetts Institute of Technology
*6:00:* **Riemann Problems for the 2-D Burgers Equation**
*Suncica Canic*, Organizer, and Barbara L. Keyfitz, University of Houston