Decay structure of two hyperbolic relaxation models with regularity loss

Abstract

This article investigates two types of decay structures for linear symmetric hyperbolic systems with nonsymmetric relaxation. Previously, the same authors introduced a new structural condition which is a generalization of the classical Kawashima–Shizuta condition and also analyzed the weak dissipative structure called the regularity-loss type for general systems with nonsymmetric relaxation, which includes the Timoshenko system and the Euler–Maxwell system as two concrete examples. Inspired by the previous work, we further construct in this article two more complex models which satisfy some new decay structure of regularity-loss type. The proof is based on the elementary Fourier energy method as well as the suitable linear combination of different energy inequalities. The results show that the model of type I has a decay structure similar to that of the Timoshenko system with heat conduction via the Cattaneo law, and the model of type II is a direct extension of two models considered previously to the case of higher phase dimensions.