Nonlinear Conservation Laws
by
Suncica Canic
University of Houston

In this talk I will present some recent developments in the theory of systems of conservation laws with the focus on two applications. The first is in the area of multi-dimensional systems od conservation laws. It addressess a benchmark problem in nonlinear wave interactions: the problem of shock reflection by a wedge (also related to the stability of transonic shocks arising around a wing of an aircraft traveling at supersonic speeds). A novel theoretical approach toward proving existence and structure of solutions will be presented. The second application is in the area of one-dimensional systems of conservation laws. This applications is related to a problem in hemodynamics: modeling of treatement of aortic abdominal aneurysm. A simple model will be presented and several open questions will be discussed. Movies showing numerical simulations will be presented.

Date received: May 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-83.