Moore-Gibson-Thompson equation with memory in a history framework: a semigroup approach

This paper is concerned with existence and uniform (exponential) stability results for a Moore-Gibson-Thompson equation with memory recently introduced by Lasiecka and Wang (Z. Angew. Math. Phys. 67(2):17, 2016) that proposed the model in a past history framework. Whereas the authors study the problem with null history, say with finite memory, here our main goal is to prove the uniform stability of the Moore-Gibson-Thompson model encompassing three different types of memory in a history space setting and using the linear semigroup theory. Therefore, our results complement those ones provided by the authors to the case of finite memory. In addition, our results also give a first answer, in some way, for some "heuristics" raised in the literature for the MGT equation when the memory term depends only on the velocity, by exemplifying that in this case the system may not be dissipative under the presence of memory.