Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

Abstract

AbstractThis study aims to investigate the well‐posedness and stability of a thermoelastic Timoshenko system with non‐Fourier heat conduction. Specifically, we analyze the system using the dual‐phase‐lag (DPL) model, which incorporates two thermal relaxation times, and , to model non‐instantaneous heat propagation. Applying the semigroup approach, we demonstrate the existence and uniqueness of the solutions. Subsequently, we introduce a novel stability parameter using the multiplier method. Exponential decay is proven for the case of with . Using Gearhart–Prüss theorem, we show the lack of exponential stability when and . Numerically, we present a fully discrete approximation using the finite element method and the backward Euler scheme, and we provide some numerical simulations to show the discrete energy decay and the behavior of solutions.