Abstract:

In this paper, we study the long-time dynamic behavior of solutions for the non-autonomous classical reaction-diffusion equation with nonlinear boundary conditions and fading memory, where the internal nonlinearity and boundary nonlinearity adheres to polynomial growth of arbitrary order as well as the balance condition. In addition, the forcing term is translation bounded, rather than translation compact, by use of contractive function method and process theory. The existence and the topological structure of uniform attractors in $L^{2}(\Omega)\times L_\mu^2(\mathbb R^+; H_{0}^1(\Omega))$ are proven. This result extends and improves existing research in the literature.

Key words: non-autonomous classical reaction-diffusion equation, uniform attractors, nonlinear boundary, fading memory, polynomial growth of arbitrary order