Asymptotic behavior of non-autonomous Lamé systems with subcritical and critical mixed nonlinearities. (October 2022)

• Record Type: Journal Article
• Authors: Costa, Alberto L.C.; Freitas, Mirelson M.; Wang, Renhai
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Lamé system -- Pullback attractors -- Upper-semicontinuity -- Critical nonlinearity -- Non-autonomous dynamical systems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103603
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with the asymptotic behavior of solutions to a class of non-autonomous Lamé systems modeling the physical phenomenon of isotropic elasticity. The main feature of this model is that the nonlinearity can be decomposed into a subcritical part and a critical one. We first show that the system generates a non-autonomous dynamical system, and then prove that the system has a minimal universe pullback attractor. The upper-semicontinuity of these pullback attractors is also established as the perturbation parameter of the external force tends to zero. The quasi-stability ideas developed by Chueshov and Lasiecka (2010, 2008, 2015) are used to prove the pullback asymptotic compactness of the solutions in order to overcome the difficulty caused by the critical growthness of the nonlinearity.