Long-time dynamics and upper-semicontinuity of attractors for a porous-elastic system with nonlinear localized damping

In this article we consider a one-dimensional porous-elastic system with nonlinear localized damping acting in an arbitrarily small region of the interval under consideration. We prove the existence of a smooth global attractor with finite fractal dimension and the existence of exponential attractors via quasi-stability theory recently proposed by Chueshov and Lasiecka. We also prove the continuity of the attractors with respect to two parameters in a residual dense set. Finally, we prove that the family of global attractors is upper-semicontinuous with respect to small perturbations of external forces. These aspects were not previously considered for porous-elastic system with localized damping. For more information see https://ejde.math.txstate.edu/Volumes/2025/11/abstr.html