Attractors of non-autonomous reaction–diffusion equations

In this paper, a new theorem which is proved in Lu et al (2005 Discrete Contin. Dyn. Syst. 8 701–19) is applied to some nonlinear reaction–diffusion equation with normal external forces (see definition 3.1.), which is translation bounded but not translation compact. We obtain the existence of the uniform attractor in H01 without any restriction on the growing order of the nonlinear term. The uniform attractor attracts all bounded subsets of H01 in the norm of H01. Then the structure of the uniform attractor is obtained by constructing skew-product flow on the extended phase space with weak topology