We study a temporally third order (Moore-Gibson-Thompson) equation with a memory term. Previously it is known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known that the ener
gy has exponential decay if the memory kernel decays exponentially. The current work is a generalization of the previous one (Part I) in that it allows the memory kernel to be more general and shows that the energy decays the same way as the memory kernel does, exponentially or not.
We are interested in the Moore-Gibson-Thompson(MGT) equation with memory begin{equation} onumber tau u_{ttt}+ alpha u_{tt}+c^2A u+bA u_t -int_0^tg(t-s)A w(s)ds=0. end{equation} We first classify the memory into three types. Then we study how a memory
term creates damping mechanism and how the memory causes energy decay.
