Global attractors for porous elastic system with memory and nonlinear frictional damping

Abstract

This paper is concerned with the long‐time behavior of a porous‐elastic system with infinite memory and nonlinear frictional damping. We prove that the dynamical system generated by the solutions of the equations is dissipative, only under the basic conditions (for the well‐posedness) on the memory kernel and the frictional damping . Further, we come up with a condition on , being more general than the usual one (with a positive constant ), under which we prove the asymptotic smoothness and quasi‐stability (the latter needs some stronger condition on ) of the dynamical system. Accordingly, we obtain the existence of a global attractor and show the finite dimensionality of the attractor.