Calculus of Variations and Geometric Measure Theory

A. Bressan - C. De Lellis

A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws

created by delellis on 26 May 2023



Inserted: 26 may 2023
Last Updated: 26 may 2023

Pages: 11
Year: 2023


Given a strictly hyperbolic $n\times n$ system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of vanishing viscosity approximations. Aim of this note is to prove that every weak solution taking values in the domain of the semigroup, and whose shocks satisfy the Liu admissibility conditions, actually coincides with a semigroup trajectory.

Keywords: uniqueness, conservation laws, Hyperbolic systems