Attractors Of Non-autonomous Reaction Diffusion Equations In Unbounded Domains

In this master's dissertation, we mainly consider the following long time behavior of non-autonomous reaction-diffusion equations in unbounded domain. Where nonlinear f satisfied with condition of increase-order, g∈Lb2(R,L2 (Rn)) is not translation tight functions but translation bounded.On theory, we give the basic concept and structure of uniform attractors in Chapter Two and on this basis prove the asymptotic compactness in unbounded domain. To further characterize the structure of uniform attractors, we promote the concept of strong and weak continuous semigroup from bounded domain to unbounded domain. We construct corresponding distinguished theorem of the existence of the uniform attractors and propose the corresponding strong and weak continuous progress.To prove the necessary compactness of process for non-autonomous system (I) in unbounded domain, we present a new approach suitable for verifying the compactness of the induction process of evolution equation in Chapter Three, which is asymptotic priori estimate.As a specific application, in Chapter Four we initially prove the asymptotic compactness of process in (L2 (Rn), L2(Rn)) and (L2 (Rn),Lp (Rn)) are the key point of compact uniform attractors for corresponding process, which is under such conditions that with critical nonlinearity on the nonlinear damping of non-autonomous reaction-diffusion equations and that the external force term is not translation compact. Then we get the existence of the uniform attractors by using abstract theorems in Chapter Three.