Spatial decay estimates for the coupled system of wave-plate type with thermal effect

Jincheng Shi; Yan Liu; Jincheng Shi; Yan Liu

doi:10.3934/math.2025016

AIMS Mathematics

2025, Volume 10, Issue 1: 338-352. doi: 10.3934/math.2025016

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Research article

Spatial decay estimates for the coupled system of wave-plate type with thermal effect

Jincheng Shi ¹,
Yan Liu ^{2
,
,}

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

Received: 22 October 2024 Revised: 24 December 2024 Accepted: 03 January 2025 Published: 08 January 2025
MSC : 35B44, 35B33

In this article, we investigate the spatial decay estimates for the biharmonic conduction equations within a coupled wave-plate system incorporating thermal effects in a two-dimensional cylindrical domain. Using the method of a second-order differential inequality, we can obtain the spatial decay estimates result for these equations. When the distance tends to infinity, the energy can decay exponentially. This result shows us that the Saint-Venant principle is also valid for the hyperbolic-parabolic coupled system.
- spatial decay estimates,
- wave-plate type with thermal effect,
- hyperbolic-parabolic coupled equations,
- Saint-Venant principle
Citation: Jincheng Shi, Yan Liu. Spatial decay estimates for the coupled system of wave-plate type with thermal effect[J]. AIMS Mathematics, 2025, 10(1): 338-352. doi: 10.3934/math.2025016

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Abstract

In this article, we investigate the spatial decay estimates for the biharmonic conduction equations within a coupled wave-plate system incorporating thermal effects in a two-dimensional cylindrical domain. Using the method of a second-order differential inequality, we can obtain the spatial decay estimates result for these equations. When the distance tends to infinity, the energy can decay exponentially. This result shows us that the Saint-Venant principle is also valid for the hyperbolic-parabolic coupled system.

References

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