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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
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.Recording: http://mm.math.cmu.edu/recordings/cna/luis_silvestre_small.mp4Date: Thursday, March 22, 2018Time: 4:30 pmLocation: Wean Hall 7218Submitted by: Ian Tice |