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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Nicholas Leger
Carnegie Melllon University
Title: Relative entropy and the stability of shocks for systems of conservation laws

Abstract: We develop a theory based on relative entropy to show the stability and uniqueness of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of big amplitude), among bounded entropic weak solutions having an additional strong trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.

Date: Tuesday, September 7, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  Dejan Slepcev