Consistent Stability Of The Moore-Gibson-Thompson Equation With Long-term Memory Terms

This paper is concerned with Moore-Gibson-Thompson(MGT)equation of the initialboundary data problem with a long-time memory term:(?)In the initial data and the memory kernel under appropriate assumptions,we given that the energyfunctional of decay rate depends on the memory kernel function.This paper is divided into two parts:The first,when memory kernel function is exponential decay,using multiplicr methodconstructs nergy functional,and constructs auxiliary functional,then exponential decay of the energy functional is obtained by precise estimates.The second,when memory kernel function is general decay,using multiplier method constructs energy functional,and constructs auxiliary functional,then through the precise estimates get general decay of the energy functional.This paper show that the decay rate of energy functional only decided by memory kernel.If memory kernel decays exponentially,then the energy decays exponentially too;If memory kernel decays generally,then the energy decays generally too.