Exponential and polynomial decay results for a swelling porous elastic system with a single nonlinear variable exponent damping: theory and numerics

We consider a swelling porous elastic system with a single nonlinear variable exponent damping. We establish the existence result using the Faedo-Galerkin approximations method, and then, we prove that the system is stable under a natural condition on the parameters of the system and the variable exponent. We obtain exponential and polynomial decay results by using the multiplier method, and these results generalize the existing results in the literature. In addition, we end our paper with some numerical illustrations.