Unique Solutions to Hyperbolic Conservation Laws with a Strictly Convex Entropy

Meeting Details

For more information about this meeting, contact Rachel Weaver, Toan T. Nguyen.

Speaker: Graziano Guerra, Università degli Studi di Milano-Bicocca

Abstract: Consider a strictly hyperbolic system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation. If the system admits a strictly convex entropy, we give a short proof that every entropy weak solution taking values within the domain of the semigroup coincides with a semigroup trajectory. Combined with a compactness argument, the result yields a uniform convergence rate for a very wide class of approximation algorithms. Some partial estimates on the convergence rate will be discussed.

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Room Reservation Information

Room Number: 114 McAllister

Date: 04/30/2025

Time: 2:30pm - 3:30pm