Attractors for nonclassical diffusion equations with dynamic boundary conditions. (June 2020)

• Record Type: Journal Article
• Authors: Lee, Jihoon; Toi, Vu Manh
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35A01 -- 35K57 -- 35B40 -- 35B41 -- 37L30; Nonclassical diffusion equation -- Dynamic boundary condition -- Global attractors -- Upper semicontinuity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111737
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the asymptotic behavior of solutions for a class of nonclassical diffusion equation ∂ t ( u − ε Δ u ) − Δ u + κ u + f ( u ) = g in a smooth bounded domain Ω in R N ( N ≥ 3 ) with dynamic boundary condition ∂ t ( u − ε Δ Γ u ) + ∂ n ( ε ∂ t u + u ) − Δ Γ u + f Γ ( u ) = g Γ on Γ = ∂ Ω . Under a Sobolev type growth condition of the nonlinear functions, we prove the existence and uniqueness of weak solution for the problem by using the Galerkin approximation method, and then establish the existence and upper semicontinuity of global attractors A ε at ε 0 ∈ [ 0, 1 ] by using the asymptotic a priori estimate method.