Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains
Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains
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DOI：
10.1016/j.jmaa.2014.03.037
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发表时间：
2013-09
影响因子：
1.3
通讯作者：
Andrew L. Krause;Bixiang Wang
中科院分区：
文献类型：
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作者：
Andrew L. Krause;Bixiang Wang
研究了定义在全空间Rn上的随机p-Laplace方程的拉回吸引子.首先建立了L2（Rn）中方程的渐近紧性，然后证明了非自治随机吸引子的存在唯一性.如果非自治的确定性强迫是时间周期的，则该吸引子是路径周期的。Sobolev嵌入在Rn上的非紧性的困难被有界区域外的解的一致小性所克服。
This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R n. We first establish the asymptotic compactness of the equation in L 2 (R n) and then prove the existence and uniqueness of non-autonomous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on R n is overcome by the uniform smallness of solutions outside a bounded domain.