@article{Shi2026, 
author = {Jincheng Shi and Zijun Cheng},
title = {Exponential spatial decay estimates for the MGT-Fourier system in semi-infinite cylindrical domains},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {19921-19937},
keywords = {Moore-Gibson-Thompson equation, Fourier heat equation, spatial decay, Saint-Venant principle, semi-infinite cylinder, energy functional},
url = {https://www.sciopen.com/article/10.3934/math.2026808},
doi = {10.3934/math.2026808},
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              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.}
}