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.