Global solvability and decay estimates for a type III thermo‐viscoelastic coupled system with infinite memory and boundary interaction feedback

Abstract

A type III thermo‐viscoelastic coupled system with infinite memory and distributed delay is considered. The interaction feedback between the nonlinear damping and the acoustic conditions are reacted on portion of the boundary. We obtain the well posedness and regularity of the system by using semigroup theory which is combined with Schauder's fixed point theorem. Moreover, the general decay estimates are established under a much larger class of relaxation functions. Our results are obtained without the boundedness condition of initial data assumed in many earlier papers in the literature. This work generalizes the composite stability between infinite memory and nonlinear damping.