Global existence and general decay of Moore–Gibson–Thompson equation with not necessarily decreasing kernel

Abstract

In this paper, we consider the Moore.Gibson.Thompson equations. By using the potential well theory we obtain the existence of a global solution. Then, we prove the general decay result of solutions under weaker assumptions than the ones frequently used in the literature. In particular, the kernels we are considering are not necessarily exponentially decaying to zero as was assumed before. The present results improve also a previous work of the authors.