Spatial Decay Estimates for Elastic Plate System With Type II Heat Conduction

The classical Saint-Venant principle has been extensively studied for harmonic and biharmonic models but remains largely unexplored for thermomechanical plates governed by hyperbolic (Type II) heat conduction, a conservative thermal model with unique dynamical features. This paper investigates the spatial decay properties of solutions to such a coupled hyperbolic elastic plate system. By constructing a novel energy functional and establishing an integral-differential inequality that it satisfies, we derive explicit exponential decay estimates in the spatial variable. The key contribution of this work is extending the Saint-Venant principle to plates with Type II heat conduction, proving that far-field disturbances decay exponentially even under conservative thermal coupling. These findings broaden the applicability of Saint-Venant-type analysis to a wider range of thermomechanical models.