Mathematics – Analysis of PDEs
Scientific paper
2012-02-10
Mathematics
Analysis of PDEs
References added
Scientific paper
We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors and asymptotic compactness for such systems. We then prove a sufficient and necessary condition for existence of pullback attractors. We also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors. For random systems containing periodic deterministic forcing terms, we show the pullback attractors are also periodic. As an application of the abstract theory, we prove the existence of a unique pullback attractor for Reaction-Diffusion equations on $\R^n$ with both deterministic and random external terms. Since Sobolev embeddings are not compact on unbounded domains, the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions.
No associations
LandOfFree
Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-237710