Uniform attractor for the partly dissipative nonautonomous lattice systems
The authors consider a general system of discrete (lattice) reaction-diffusion equations with a source term. They prove the existence of a uniform attractor for this system, when the source term is locally square integrable in time, asymptotically small and translation bounded but not translation compact. They show that the family of processes corresponding to the nonautonomous lattice system with source terms belonging to weak closure of translation set of locally asymptotically small functions possesses a uniform attractor, which is also identified with the original attractor. The upper semicontinuity of the uniform attractor is also proved. The paper also contains a review of the recent literature on the existence of uniform attractors in the partial and lattice differential equations.
scientific article; zbMATH DE number 5629334
scientific article