Moore–Gibson–Thompson equation with memory, part II: General decay of energy

We study a temporally third order (Moore–Gibson–Thompson) equation with a memory term. Previously it was known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known that the energy 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.