Decay property for symmetric hyperbolic system with memory-type diffusion

Mari Okada; Naofumi Mori; Shuichi Kawashima

doi:10.1016/j.jde.2020.12.021

Decay property for symmetric hyperbolic system with memory-type diffusion

Mari Okada, Naofumi Mori, Shuichi Kawashima

国際理工学センター（理工学術院）

研究成果: Article › 査読

抄録

We study the decay property for symmetric hyperbolic systems with memory-type diffusion. Under the structural condition (called Craftsmanship condition) we prove that the system is uniformly dissipative and the solutions satisfy the corresponding decay property. Our proof is based on a technical energy method in the Fourier space which makes use of the properties of strongly positive definite kernels.

本文言語	English
ページ（範囲）	287-317
ページ数	31
ジャーナル	Journal of Differential Equations
巻	276
DOI	https://doi.org/10.1016/j.jde.2020.12.021
出版ステータス	Published - 2021 3 5

ASJC Scopus subject areas

Analysis
Applied Mathematics

文献へのアクセス

10.1016/j.jde.2020.12.021

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引用スタイル

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abstract = "We study the decay property for symmetric hyperbolic systems with memory-type diffusion. Under the structural condition (called Craftsmanship condition) we prove that the system is uniformly dissipative and the solutions satisfy the corresponding decay property. Our proof is based on a technical energy method in the Fourier space which makes use of the properties of strongly positive definite kernels.",

keywords = "Decay property, Energy method, Memory-type dissipation, Strongly positive definite kernels, Symmetric hyperbolic systems",

author = "Mari Okada and Naofumi Mori and Shuichi Kawashima",

note = "Funding Information: S. Kawashima is partially supported by JSPS KAKENHI Grant Numbers JP18H01131 and JP19H05597 .",

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AU - Mori, Naofumi

AU - Kawashima, Shuichi

N1 - Funding Information: S. Kawashima is partially supported by JSPS KAKENHI Grant Numbers JP18H01131 and JP19H05597 .

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N2 - We study the decay property for symmetric hyperbolic systems with memory-type diffusion. Under the structural condition (called Craftsmanship condition) we prove that the system is uniformly dissipative and the solutions satisfy the corresponding decay property. Our proof is based on a technical energy method in the Fourier space which makes use of the properties of strongly positive definite kernels.

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KW - Energy method

KW - Memory-type dissipation

KW - Strongly positive definite kernels

KW - Symmetric hyperbolic systems

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