Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact 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