Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory

Abstract

We consider the well-posedness and the long time behavior of the Moore– Gibson–Thompson equation with memory in the critical case. We first find general sufficient conditions that guarantee a (optimal) polynomial decay of the system. Then by comparing the behavior of the resolvent of the Moore–Gibson–Thompson system with the one of the resolvent of the wave equation with a frictional interior damping, we furnish a stronger polynomial decay of the solution.