53rd Midwest PDE Seminar March 19-21, 2004 Department of Mathematics University of Missouri

Barbara Lee Keyfitz University of Houston
Hyperbolic conservation laws, degenerate elliptic equations and free boundary problems

Abstract

Self-similar reduction of an important class of two-dimensional conservation laws leads to boundary value problems for equations which change type. We have established a method for solving free boundary problems for quasilinear degenerate elliptic equations which arise when shocks interact with the subsonic (nonhyperbolic) part of the solution.

This research was carried out jointly with Suncica Canic, Eun Heui Kim and Gary Lieberman.