Conservation Laws with no Classical Riemann Solutions: Existence of Singular Shocks

Dr. Charis Tsikkou

Department of Mathematics
The Ohio State University

24 February 2012
Shelby Center 218
3:00 (Refreshements at 2:30)

Abstract

Conservation laws are the most fundamental principles of continuum mechanics. The basic tool in the construction of solutions to the Cauchy problem for conservation laws with smooth initial data is the Riemann problem. It consists of piecewise constant initial data having a single discontinuity at the origin.

In this talk I will review the results obtained for the solutions to the Riemann problem and present a system of two equations derived from isentropic gas dynamics with no classical solution. I will then use the blowing-up approach to geometric singular perturbation problems to show that the system exhibits unbounded solutions (singular shocks) with Dafermos profiles.