Speaker: Alberto Bressan, Penn State University

Title: Hyperbolic conservation laws: past and future

Abstract: This talk will survey some old and new results in the fundamental theory of one-dimensional hyperbolic systems of conservation laws.  After reviewing basic results on the existence and continuous dependence of weak solutions (in distributional sense), the talk will cover the most  recent advances concerning the uniqueness of entropy admissible solutions.  Implications of these results toward a posteriori error estimates for numerical approximations will be discussed, together with various open questions

Bio: Alberto Bressan completed his undergraduate studies at the University of Padova, Italy, in 1978, and received a Ph.D. from the University of Colorado, Boulder, in 1982. He has held faculty positions at the University of Colorado, Boulder, and at the International School for Advanced Studies in Trieste, Italy. Presently he is the Eberly Family Chair Professor of Mathematics at the Pennsylvania State University. His scienti c interests lie mainly in the areas of nonlinear PDEs, optimization and control theory, di erential games, and hyperbolic systems of conservation laws. A. Bressan delivered a plenary lecture at the International Congress of Mathemati- cians, Beijing 2002. He received various awards, including the A. Feltrinelli prize for Mathematics, Mechanics, and Applications, from the Accademia Nazionale dei Lincei in Rome, 2006, He received the S.I.A.M. \Analysis of Partial Di erential Equations" prize in 2007, the M. B^ocher prize from the American Mathematical Society in 2008, and the G. Fichera prize from the Unione Matematica Italiana in 2011. He currently serves on the editorial board of 16 mathematical journals. 1

This talk will be offered in a hybrid format. If you wish to participate remotely, please send an email to [email protected].