Existence and decay rates of solution for the Moore-Gibson-Thompson equation linear

This work is devoted to the study the linear Moore-Gibson-Thompson equation with a viscoelastic memory. Under some appropriate assumptions on the relaxation function $g$ and with certain initial data, the existence and uniqueness of a local solution are obtained via Faedo--Galerkin's method. The global existence of solutions is also established. Furthermore, we prove the decay rates for the energy of Moore-Gibson-Thompson equation linear with a viscoelastic memory of relaxation kernels.