Calculus of Variations and Geometric Measure Theory

A regularity result for strictly hyperbolic, genuinely non-linear systems of conservation laws in one space dimension, I

Laura Caravenna (Padova)

created by magnani on 12 Jan 2011

19 jan 2011


Dipartimento di Matematica - Sala Seminari - ore 17:00

ABSTRACT: We discuss in two talks a regularity issue for entropy solutions of a class of systems of scalar conservation laws in one space dimension.

This first talk will be devoted to introducing the setting and the main assumptions (e.g. strict hyperbolicity and characteristic families, the decomposition into wave measures). A few fundamental results on hyperbolic systems of conservation laws in one space dimension will be recalled, as the Lax’s solution to the Riemann problem and Bressan’s existence and uniqueness of a Lipschitz semigroup of solutions for small BV initial data. Examples will be given in the case of a single conservation law.