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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Luis Silvestre
University of Chicago
Title: Regularity and structure of scalar conservation laws

Abstract: Scalar conservation law equations develop jump discontinuities even when the initial data is smooth. Ideally, we would expect these discontinuities to be confined to a collection of codimension-one surfaces, and the solution to be relatively smoother away from these jumps. The picture is less clear for rough initial data which is merely bounded. While a linear transport equation may have arbitrarily rough solutions, genuinely nonlinear conservation laws have a subtle regularization effect. We prove that the entropy solution will become immediately continuous outside of a codimension-one rectifiable set, that all entropy dissipation is concentrated on the closure of this set, and that the $L^\infty$ norm of the solution decays at a certain rate as t goes to infinity.

Date: Thursday, March 22, 2018
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice