Uniform attractors for the closed process and applications to the reaction-diffusion equation with dynamical boundary condition

Abstract

In this paper, we first introduce the concept of a closed process in a Banach space, and we obtain the structure of a uniform attractor of the closed process by constructing a skew product-flow on the extended phase space. Then, the properties of the kernel section of closed process are investigated. Moreover, we prove the existence and structure of the uniform attractor for the reaction-diffusion equation with a dynamical boundary condition in L p without any restriction on the growth order of the nonlinear term.