Limiting dynamics in one-dimensional porous-elasticity

Abstract

In this paper we investigate the long-term behavior of the solutions of the one-dimensional porous-elasticity problem with porous dissipation and nonlinear feedback force. We prove that the porous-elasticity problem converges to a quasi-static problem for the microvoids motion as a suitable parameter J tends to zero. Finite dimensional global attractor with additional regularity in J is obtained using the recent quasi-stability theory. Finally, we compare the porous-elasticity problem with quasi-static problem, in the sense of the upper-semicontinuity of their attractors as J → 0.