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Research Article | Open Access

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

Jincheng Shi1, Yan Liu2( )
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China
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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.

Keywords

spatial decay estimateswave-plate type with thermal effecthyperbolic-parabolic coupled equationsSaint-Venant principle
CLC number: 35B44, 35B33

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 338-352
DOI: 10.3934/math.2025016

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Cite this article:
Shi J, Liu Y. Spatial decay estimates for the coupled system of wave-plate type with thermal effect. AIMS Mathematics, 2025, 10(1): 338-352. https://doi.org/10.3934/math.2025016

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Received: 22 October 2024
Revised: 24 December 2024
Accepted: 03 January 2025
Published: 15 January 2025
©2025 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)