Dynamics of a one-dimensional nonlinear poroelastic system weakly damped

Abstract

In this paper, we study the long-time behavior of a nonlinear porous elasticity system. The system is subject to a viscoporous damping and a nonlinear source term which is locally Lipschitz and depends only on the volume fraction. The dynamical system associated with the solutions of the model is gradient, and under the hypothesis of equal speeds of propagation for the waves, we prove that it is also quasi-stable, which allows us to show the existence of a global attractor for the system, which is the main result of the paper.