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

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.