拉回吸引子
拉回
紧凑空间
数学
吸引子
随机动力系统
索波列夫空间
动力系统理论
强迫(数学)
数学分析
纯数学
线性系统
线性动力系统
物理
量子力学
标识
DOI:10.1016/j.jde.2012.05.015
摘要
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 under certain conditions. As an application of the abstract theory, we prove the existence of a unique pullback attractor for Reaction–Diffusion equations on Rn 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.
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