The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness

Abstract

We study the uniform global attractor for a general nonautonomous reaction-diffusion system without uniqueness using a new developed framework of an evolutionary system. We prove the existence and the structure of a weak uniform (with respect to a symbol space) global attractor $\mathcal A$. Moreover, if the external force is normal, we show that this attractor is in fact a strong uniform global attractor. The existence of a uniform (with respect to the initial time) global attractor $\mathcal A^0$ also holds in this case, but its relation to $\mathcal A$ is not yet clear due to the non-uniqueness feature of the system.