Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity. (October 2016)

• Record Type: Journal Article
• Authors: Xie, Yongqin; Li, Qingsong; Zhu, Kaixuan
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 23
• Page End: 37
• Publication Date: 2016-10
• Subjects: Asymptotic contractive semigroup -- Nonclassical diffusion equation -- Global attractor -- The whole space -- Polynomial growth of arbitrary order; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, using a new method (or technique) called "Asymptotic Contractive Semigroup Method" (seeTheorem 2.3 ) we prove the existence of global attractor for the nonclassical diffusion equations in H 1 ( R n ) . The nonlinearity satisfies the arbitrary order polynomial growth conditions and the forcing term g only belongs to H − 1 ( R n ) . The results obtained essentially improve and complement in some previously published papers.