Tel Aviv University, Applied Mathematics Seminar Date: Tuesday December 18, 2012, 15:10 Place: Schreiber Bldg, Room 309 Speaker: Michael Sever, Hebrew University Title: A Continuation of weak solutions of hyperbolic systems of conservation laws Abstract: An argument, well short of a complete proof, is given that the Cauchy problem for nonlinear, hyperbolic systems of conservation laws in more than one space dimension and time, is in general not well posed. Consideration of continuation of weak solutions of a simple form as the initial data is varied leads to a seemingly necessary estimate on the space of test functions determining the weak solution. Attempt to obtain such an estimate is seen to require an admissibility condition on discontinuities. We postulate such an admissibility condition. In one space dimension, familiar conditions are recovered, but in general the condition cannot be expected in higher dimensions. Nonetheless, we show that shocks can be admissible in this sense for reduced, relativistic Euler systems. Webpage of the applied mathematics seminar: <https://sites.google.com/site/tauamathseminar/> ______________________________________________________________________ Dr. Yoel Shkolnisky Department of Applied Mathematics School of Mathematical Sciences phone: 972-3-640-8705 Tel Aviv University, fax : 972-3-640-9357 Tel Aviv, 69978 Israel email: <yoelsh@post.tau.ac.il> ______________________________________________________________________ --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yoel Shkolnisky <yoelsh@post.tau.ac.il>