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

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.