Mathematical entropy and Euler-Cattaneo-Maxwell system

Shuichi Kawashima, Yoshihiro Ueda

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)101-143
Number of pages43
JournalAnalysis and Applications
Volume14
Issue number1
DOIs
Publication statusPublished - 2016 Jan 1
Externally publishedYes

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Keywords

  • Euler-Cattaneo-Maxwell system
  • Global solution
  • Hyperbolic balance laws
  • Mathematical entropy
  • Timoshenko system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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