Asymptotic stability for the Moore–Gibson–Thompson equation with memory

Abstract

We undertake a study of the asymptotic stability of the Moore–Gibson–Thompson equation with memory effect, which is one of the nonlinear acoustic equations describing the propagation of sound waves in gas and liquid. The effects of viscosity, thermal conductivity, and thermal radiation on acoustic wave propagation are considered in this model. The current work improves the previously related results in that it removes the convexity assumption on the memory kernels and obtains the uniform decay rate $t^{-1}$ of solution energy to the Moore–Gibson–Thompson equation, with only basic conditions on the memory kernels (without any decay conditions).