Higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation in non-cylindrical domains. (January 2015)

• Record Type: Journal Article
• Authors: Xiao, Yanping; Sun, Chunyou
• Is Part Of: Nonlinear analysis. Volume 113(2015)
• Page Start: 309
• Page End: 322
• Publication Date: 2015-01
• Subjects: 35K57 -- 35L05 -- 35B40 -- 35B41; Non-cylindrical domains -- Pullback attractor -- Higher-order asymptotic attraction -- Reaction–diffusion equation -- Variational solution; 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.2014.10.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the higher-order asymptotic attraction of pullback attractors for a reaction–diffusion equation with domains expanding in time. Firstly, to make the test functions meaningful, a maximum principle is proved for the corresponding variational solution; then, we establish some higher-order integrability results about the difference of variational solutions, and finally we prove the main result that the known ( L 2, L 2 ) pullback D λ -attractor can attract indeed the D λ class in L q -norm for any q ∈ [ 2, + ∞ ) .