Quasi-stability and attractors for a porous-elastic system with history memory. Issue 17 (22nd November 2022)

• Record Type: Journal Article
• Authors: Feng, B.; Freitas, M. M.; Almeida Júnior, D. S.; Ramos, A. J. A.
• Is Part Of: Applicable analysis. Volume 101:Issue 17(2022)
• Page Start: 6237
• Page End: 6254
• Publication Date: 2022-11-22
• Subjects: Porous elastic system -- memory -- quasi-stable systems -- attractor; 35B40 -- 35B41 -- 74Dxx; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1921154
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The paper is concerned with a porous elastic problem in a past history framework. We study its long-time behavior through the corresponding autonomous dynamical system. Instead of showing the directly the system has a bounded absorbing set, we show the system is gradient system and asymptotic smoothness, and prove the existence of a global attractor, which is characterized as unstable manifold of the set of stationary solutions. We also get the quasi-stability of the system by establishing a stabilizability inequality and therefore obtain the finite fractal dimension of the global attractor.