Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system

In this paper, we consider a one-dimensional thermoelastic porous system with memory effect. We establish the existence and uniqueness result using the Faedo Galerkin approximations method. Then, we prove a general decay result under a very general assumption on the relaxation function and for suitable initial data with enough regularities. In order to validate our theoretical results, we discretize our system using hybrid numerical scheme and we present several numerical experiments and tests.