Global existence and exponential decay for a swelling porous-heat system subject to a distributed delay

In this article, we consider a swelling porous-heat system with viscous damping and distributed delay term. It’s well-known in the literature that the thermal effect only lacks exponential stability. For that, we need to add another damping mechanism to stabilize exponentially the system. However, we prove, based on the energy method, that the combination of viscous damping and thermal effect provokes an exponential stability in the presence of distributed delay irrespective of the wave speeds of the system.