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

Abstract

We consider a swelling porous-elastic system with a single nonlinear variable exponent damping. 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.AMS Subject Classifications: 93D20; 35B40.

Global existence and stability results of a nonlinear swelling soil system with nonlinear source terms of variable exponent types

“…Recently, Sofyan et. al [16] established for the first time exponential and polynomial decay results for swelling soils of the form…”