Spatial decay estimate for the MGT-Fourier model on a semi-infinite cylinder in $ \mathbb{R}^2 $

Xuejiao Chen; Zijun Cheng; Xuejiao Chen; Zijun Cheng

doi:10.3934/era.2026167

Electronic Research Archive

2026, Volume 34, Issue 6: 3696-3712. doi: 10.3934/era.2026167

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Research article

Spatial decay estimate for the MGT-Fourier model on a semi-infinite cylinder in $ \mathbb{R}^2 $

Xuejiao Chen ¹,
Zijun Cheng ^{2
,
,}

1.
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
2.
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 511201, China

Received: 26 March 2026 Revised: 21 April 2026 Accepted: 27 April 2026 Published: 30 April 2026

This study investigates the spatial decay estimate for a coupled Moore-Gibson-Thompson (MGT)-Fourier system on a semi-infinite cylinder in $ \mathbb{R}^2 $. The system is comprised of a third-order MGT displacement equation and a parabolic heat equation with symmetric coupling. Using a weighted energy functional and an integral-differential inequality, we establish the exponential decay along the axial direction. This result offers a generalized Saint-Venant principle for coupled dissipative thermoviscoelastic models, thus extending the classical analysis to higher-order systems and advancing our understanding of MGT equations in an unbounded domain.
- Saint-Venant principle,
- MGT-Fourier model,
- integral-differential inequality,
- semi-infinite cylinder
Citation: Xuejiao Chen, Zijun Cheng. Spatial decay estimate for the MGT-Fourier model on a semi-infinite cylinder in $ \mathbb{R}^2 $[J]. Electronic Research Archive, 2026, 34(6): 3696-3712. doi: 10.3934/era.2026167

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Abstract

This study investigates the spatial decay estimate for a coupled Moore-Gibson-Thompson (MGT)-Fourier system on a semi-infinite cylinder in $ \mathbb{R}^2 $. The system is comprised of a third-order MGT displacement equation and a parabolic heat equation with symmetric coupling. Using a weighted energy functional and an integral-differential inequality, we establish the exponential decay along the axial direction. This result offers a generalized Saint-Venant principle for coupled dissipative thermoviscoelastic models, thus extending the classical analysis to higher-order systems and advancing our understanding of MGT equations in an unbounded domain.

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