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Research Article | Open Access

Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

Zihan Cai1, Yan Liu1, Baiping Ouyang2( )
Department of Applied Mathematics, Guangdong University of Finance, Yingfu Road, Guangzhou 510521, China
College of Data Science, Guangzhou Huashang College, Huashang Road, Guangzhou 511300, China
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Abstract

In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of L p − L q are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.

Keywords

thermoelastic plate equationsnon-local operatordecay propertiesregularity-lossWentzel-Kramers-Brillouin (WKB) analysisfractional power operators
CLC number: 35B40, 35M31, 35Q74, 74F05

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 260-275
DOI: 10.3934/math.2022017

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Cite this article:
Cai Z, Liu Y, Ouyang B. Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations. AIMS Mathematics, 2022, 7(1): 260-275. https://doi.org/10.3934/math.2022017

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Received: 13 July 2021
Accepted: 27 September 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)