Pullback attractors for non‐autonomous porous elastic system with nonlinear damping and sources terms

Abstract

In this paper, we study the asymptotic behavior of a non‐autonomous porous elastic systems with nonlinear damping and sources terms. By employing nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. We also prove the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the sources terms. Finally, we prove the upper‐semicontinuity of pullback attractors with respect to non‐autonomous perturbations.

Dynamics of a one-dimensional nonlinear poroelastic system weakly damped

“…Freitas in [16] considered the system (1.9)-(1.10) with external sources h 1 , h 2 depending on x and on t and obtained a non-autonomous dynamical system associated with the solutions of the system. In this case, the author proved the existence of minimal pullback attractors as well as the upper semicontinuity of the attractor with respect to non-autonomous perturbations.…”