Large time behavior of solutions to symmetric hyperbolic systems with non-symmetric relaxation

Abstract

This article is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima–Shizuta stability condition formulated in [8], [4]. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (cf. the Timoshenko system and the Euler–Maxwell system). Therefore our purpose of this paper is to formulate a new structural condition and to analyze the weak dissipative structure for general systems with non-symmetric relaxation. This article is a survey of the paper [5].