Attractors for nonautonomous reaction–diffusion systems with symbols without strong translation compactness

Article type: Research Article

Authors: Lu, Songsong

Affiliations: Department of Mathematics, Huazhong Normal University, Wuhan, Hubei, 430079, P.R. China and Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, P. R. China. E-mail: songsong_lu@yahoo.com

Abstract: The long time behavior of the solutions of a general reaction–diffusion system (RDS) that covers many examples, such as the RDS with polynomial nonlinearity and Ginzburg–Landau equation, is discussed. First, the existence of a compact uniform attractor 𝒜0 in H is proved without additional assumptions on the interaction functions. Then the structure of the attractor is obtained for a certain class of interaction functions without strong translation compactness. For instance, the interaction functions are not required to be uniformly continuous. Moreover, an interesting problem arises naturally from this paper.

Keywords: uniform attractor, reaction–diffusion system, normal symbol

Journal: Asymptotic Analysis, vol. 54, no. 3-4, pp. 197-210, 2007