REGULARITY OF ENTROPY SOLUTIONS TO EQUATIONS OF CONSERVATION LAWS

Carlo Bianca (1) , Christian Dogbe (2)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

This paper is devoted to the analysis of solutions of scalar conservation laws where the flux function is a x-dependent function. Specifically we prove that, under less regular fluxes, the maximum between two entropy subsolutions is also an entropy subsolution. The proof of the main result is based on the entropy method of the Kruzkhov theory, P. L. Lions and P. Souganidis methods and the regularization method of Di Perna-Lions.

Mots clés: First order PDE's; Scalar conservation law; viscosity solutions; regularity

Domaines: Equations aux dérivées partielles [math.AP]

Carlo Bianca, Christian Dogbe. REGULARITY OF ENTROPY SOLUTIONS TO EQUATIONS OF CONSERVATION LAWS. Nonlinear Studies, 2019, 26, pp.129-157. ⟨hal-02151609⟩