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

Zihan Cai; Yan Liu; Baiping Ouyang; Zihan Cai; Yan Liu; Baiping Ouyang

doi:10.3934/math.2022017

AIMS Mathematics

2022, Volume 7, Issue 1: 260-275. doi: 10.3934/math.2022017

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Research article

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

1.
Department of Applied Mathematics, Guangdong University of Finance, Yingfu Road, Guangzhou 510521, China
2.
College of Data Science, Guangzhou Huashang College, Huashang Road, Guangzhou 511300, China

Received: 13 July 2021 Accepted: 27 September 2021 Published: 11 October 2021
MSC : 35B40, 35M31, 35Q74, 74F05

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.
- thermoelastic plate equations,
- non-local operator,
- decay properties,
- regularity-loss,
- Wentzel-Kramers-Brillouin (WKB) analysis,
- fractional power operators
Citation: Zihan Cai, Yan Liu, Baiping Ouyang. Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations[J]. AIMS Mathematics, 2022, 7(1): 260-275. doi: 10.3934/math.2022017

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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.

References

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