General boundary stabilization of memory-type thermoelasticity

In this paper we consider an n -dimensional system of thermoelasticity, where a viscoelastic dissipation is acting on a part of the boundary. By using a lemma, first appeared in the work of Messaoudi and Soufyane [“General decay of solutions of a wave equation with a boundary control of memory type,” Nonlinear Anal.: Real World Appl. (to be published)], we establish a general decay result, from which the usual exponential and polynomial decay are only special cases. Our result improves earlier ones in the literature and extends the general result of Messaoudi and Soufyane [“General decay of solutions of a wave equation with a boundary control of memory type,” Nonlinear Anal.: Real World Appl. 11, 2896 (2010] to thermoelastic systems.