Global and exponential attractors for mixtures of solids with Fourier's law. (February 2022)

• Record Type: Journal Article
• Authors: Freitas, M.M.; Ramos, A.J.A.; Júnior, D.S. Almeida; Aum, P.T.P.; Almeida, J.L.L.
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Mixture of solids -- Fourier law -- Global attractors -- Exponential attractors; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103391
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper presents a study of the long-time dynamics of the dynamical system generated by a nonlinear system modeling mixture of solids with nonlinear damping and Fourier's law. By using the recent quasi-stability theory, we prove the existence of a smooth finite dimensional global attractor, which is characterized as an unstable manifold of the set of stationary solutions. The quasi-stability of the system is achieved through an estimated stabilizability. Moreover, the existence of a generalized exponential attractor is shown.