Exponential spatial decay estimates for the MGT-Fourier system in semi-infinite cylindrical domains

Jincheng Shi; Zijun Cheng; Jincheng Shi; Zijun Cheng

doi:10.3934/math.2026808

AIMS Mathematics

2026, Volume 11, Issue 7: 19921-19937. doi: 10.3934/math.2026808

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Research article

Exponential spatial decay estimates for the MGT-Fourier system in semi-infinite cylindrical domains

Jincheng Shi 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, 510521, China

Received: 09 May 2026 Revised: 23 June 2026 Accepted: 30 June 2026 Published: 07 July 2026
MSC : 35B30, 35K55, 35Q35

This paper investigates the spatial decay estimates for a coupled Moore-Gibson-Thompson (MGT) and Fourier heat system defined on a semi-infinite cylindrical domain in $\mathbb{R}^3$. Under homogeneous initial-boundary conditions and suitable decay assumptions at infinity, we derive a second-order differential inequality satisfied by the total energy functional. By transforming this inequality into a first-order form via operator factorization, we establish explicit exponential decay estimates of the energy along the axial direction. The result generalizes the classical Saint-Venant principle to higher-order coupled dissipative systems and provides a quantitative characterization of spatial decay for MGT-Fourier-type equations in unbounded domains. The findings contribute to the mathematical theory of thermoviscoelasticity and offer a foundation for further studies on structural stability and long-time behavior in such coupled systems.
- Moore-Gibson-Thompson equation,
- Fourier heat equation,
- spatial decay,
- Saint-Venant principle,
- semi-infinite cylinder,
- energy functional
Citation: Jincheng Shi, Zijun Cheng. Exponential spatial decay estimates for the MGT-Fourier system in semi-infinite cylindrical domains[J]. AIMS Mathematics, 2026, 11(7): 19921-19937. doi: 10.3934/math.2026808

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Abstract

This paper investigates the spatial decay estimates for a coupled Moore-Gibson-Thompson (MGT) and Fourier heat system defined on a semi-infinite cylindrical domain in $\mathbb{R}^3$. Under homogeneous initial-boundary conditions and suitable decay assumptions at infinity, we derive a second-order differential inequality satisfied by the total energy functional. By transforming this inequality into a first-order form via operator factorization, we establish explicit exponential decay estimates of the energy along the axial direction. The result generalizes the classical Saint-Venant principle to higher-order coupled dissipative systems and provides a quantitative characterization of spatial decay for MGT-Fourier-type equations in unbounded domains. The findings contribute to the mathematical theory of thermoviscoelasticity and offer a foundation for further studies on structural stability and long-time behavior in such coupled systems.

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