Attractors of non-autonomous reaction–diffusion equations

Haitao Song, Shan Ma, Chengkui Zhong

Abstract:

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 $H_0^1$ without any restriction on the growing order of the nonlinear term. The uniform
attractor attracts all bounded subsets of $H_0^1$ in the norm of $H_0^1$. Then the structure of the uniform
attractor is obtained by constructing skew-product flow on the extended phase space with weak
topology.