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

Global Center for Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	287-317
Number of pages	31
Journal	Journal of Differential Equations
Volume	276
DOIs	https://doi.org/10.1016/j.jde.2020.12.021
Publication status	Published - 2021 Mar 5

Keywords

Decay property
Energy method
Memory-type dissipation
Strongly positive definite kernels
Symmetric hyperbolic systems

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2020.12.021

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title = "Decay property for symmetric hyperbolic system with memory-type diffusion",

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 . Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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AU - Okada, Mari

AU - Mori, Naofumi

AU - Kawashima, Shuichi

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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.

AB - 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.

KW - Decay property

KW - Energy method

KW - Memory-type dissipation

KW - Strongly positive definite kernels

KW - Symmetric hyperbolic systems

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SP - 287

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Decay property for symmetric hyperbolic system with memory-type diffusion

Abstract

Keywords

ASJC Scopus subject areas

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