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Research Article | Open Access

Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ

Jincheng Shi1, Shuman Li2, Cuntao Xiao3, Yan Liu2( )
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
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Abstract

This article focused on investigating the spatial behavior of the quasi-static biharmonic conduction equation within the framework of type Ⅲ of the second gradient in a two-dimensional cylindrical domain. The results of growth or decay estimates were established by using a second-order differential inequality. When the distance tends to infinity, the energy either grows exponentially or decays exponentially. The results showed that the Saint-Venant principle was also valid for the quasi-static biharmonic conduction equation.

Keywords

Phragmén-Lindelöf alternativequasi-static heat conductionSaint-Venant's principlespatial behaviorbiharmonic equation

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Electronic Research Archive
Volume 32 Issue 11,
November 2024
Pages 6235-6257
DOI: 10.3934/era.2024290

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Cite this article:
Shi J, Li S, Xiao C, et al. Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ. Electronic Research Archive, 2024, 32(11): 6235-6257. https://doi.org/10.3934/era.2024290

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Received: 02 October 2024
Revised: 31 October 2024
Accepted: 06 November 2024
Published: 19 November 2024
©2024 the Author(s), licensee AIMS Press.

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