Regularity of entropy solutions to a class of conservation laws

Abstract

This paper deals with the analysis of solutions of a class of conservation laws when the flux function is a $x$-dependent function. Specifically we prove that, under less regular assumptions on the flux, the maximum between two entropy subsolutions is also an entropy subsolution. The proof of the main result is based on the entropy definition of the Kruzkhov theory, the Lions-Souganidis methods and the regularization method of DiPerna-Lions.