Energy decay for a thermoelastic system with memory and boundary logarithmic damping

Abstract

This paper is devoted to the analysis of a thermoelastic system with memory and nonlinear boundary damping of logarithmic type. The model consists of a coupled system describing the interaction between elastic displacement and temperature. Under suitable assumptions on the memory kernels, we establish the well-posedness of the system and derive general energy decay estimates by constructing an appropriate Lyapunov functional and using multiplier techniques. The obtained results show that the logarithmic boundary damping, despite its weak dissipative nature, is sufficient to ensure the stabilization of the system, with decay rate governed by the properties of the relaxation functions. This work extends and strengthens several existing results in the literature.