Uniform Attractors for Nonclassical Diffusion Equations with Memory. (30th May 2016)

• Record Type: Journal Article
• Authors: Xie, Yongqin; Li, Yanan; Zeng, Ye
• Other Names: Secchi Simone Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-05-30
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/5340489
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We introduce a new method (or technique), asymptotic contractive method, to verify uniform asymptotic compactness of a family of processes. After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearity f satisfies the polynomial growth of arbitrary order and the time-dependent forcing term g is only translation-bounded in L l o c 2 ( R ; L 2 ( Ω ) ) .