Dissipative structure and asymptotic profiles for symmetric hyperbolic systems with memory

Shogo Taniue, Shuichi Kawashima*

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We study symmetric hyperbolic systems with memory-type dissipation and investigate their dissipative structures under Craftsmanship condition. We treat two cases: memory-type diffusion and memory-type relaxation, and observe that the dissipative structures of these two cases are essentially different. Namely, we show that the dissipative structure of the system with memory-type diffusion is of the standard type, while that of the system with memory-type relaxation is of the regularity-loss type. Moreover, we investigate the asymptotic profiles of the solutions for t → ∞. In the diffusion case, it is proved that the systems with memory and without memory have the same asymptotic profile for t → ∞, which is given by the superposition of linear diffusion waves. We have the same result also in the relaxation case under enough regularity assumption on the initial data.

本文言語English
ページ(範囲)453-492
ページ数40
ジャーナルJournal of Hyperbolic Differential Equations
18
2
DOI
出版ステータスPublished - 2021 6

ASJC Scopus subject areas

  • 分析
  • 数学 (全般)

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