Decay structure of two hyperbolic relaxationmodels with regularity loss

Yoshihiro Ueda, Renjun Duan, Shuichi Kawashima

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10 Citations (Scopus)


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 theweak dissipative structure called the regularityloss 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 themodel of type I has a decay structure similar to that of the Timoshenko system with heat conduction via the Cattaneo law, and themodel of type II is a direct extension of two models considered previously to the case of higher phase dimensions.

Original languageEnglish
Pages (from-to)235-292
Number of pages58
JournalKyoto Journal of Mathematics
Issue number2
Publication statusPublished - 2017 Jun
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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