Existence and asymptotic stability of solutions for a nonlinear thermoviscoelastic system with a source term involving a variable exponent

Abstract

In this paper, we investigate the asymptotic stability of solutions for a thermoviscoelastic system with a nonlinear variable exponent source term and a damping term. Using the Faedo-Galerkin method, we establish the existence of solutions. Then, applying the perturbed energy method, we demonstrate a general rate of energy decay.