A general stability result for swelling porous elastic media with nonlinear damping

Abstract

We consider a swelling porous-elastic system with a single nonlinear damping in the elastic equation. Recently, Ramos et al. [Stability results for elastic porous media swelling with nonlinear damping. J Math Phys. 2020;61(10):101505.] considered the same system and established a general decay result provided that the wave speeds of the system are equal. In this paper, we obtain the general decay result without imposing a condition on the wave speeds of the system. This is a striking and unexpected result compared to Timoshenko system, porous systems, and Laminated beams system with similar damping. We also perform some numerical tests to illustrate our theoretical results.