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

Jincheng Shi; Shuman Li; Cuntao Xiao; Yan Liu; Jincheng Shi; Shuman Li; Cuntao Xiao; Yan Liu

doi:10.3934/era.2024290

Electronic Research Archive

2024, Volume 32, Issue 11: 6235-6257. doi: 10.3934/era.2024290

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

1.
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
2.
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China
3.
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China

Received: 02 October 2024 Revised: 31 October 2024 Accepted: 06 November 2024 Published: 19 November 2024

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.
- Phragmén-Lindelöf alternative,
- quasi-static heat conduction,
- Saint-Venant's principle,
- spatial behavior,
- biharmonic equation
Citation: Jincheng Shi, Shuman Li, Cuntao Xiao, Yan Liu. Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ[J]. Electronic Research Archive, 2024, 32(11): 6235-6257. doi: 10.3934/era.2024290

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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.

References

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