Mathematical entropy and Euler–Cattaneo–Maxwell system

Abstract

In this paper, we introduce a notion of the mathematical entropy for hyperbolic systems of balance laws with (not necessarily symmetric) relaxation. As applications, we deal with the Timoshenko system, the Euler–Maxwell system and the Euler–Cattaneo–Maxwell system. Especially, for the Euler–Cattaneo–Maxwell system, we observe that its dissipative structure is of the regularity-loss type and investigate the corresponding decay property. Furthermore, we prove the global existence and asymptotic stability of solutions to the Euler–Cattaneo–Maxwell system for small initial data.