随机反应扩散方程的Lp-随机吸引子

刘林芳, 尹福其

数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 751-766.

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数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 751-766. DOI: 10.12386/A2014sxxb0070
论文

随机反应扩散方程的Lp-随机吸引子

    刘林芳, 尹福其
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Lp-Random Attractor for Stochastic Reaction-Diffusion Equation on Unbounded Domains

    Lin Fang LIU, Fu Qi YIN
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摘要

研究了定义在无界区域上具可乘白噪音的随机反应扩散方程的渐近行为.运用一致估计得到了Lp-随机吸收集；对方程的解运用渐近优先估计法，建立了相应随机动力系统的渐近紧性，证明了Lp-随机吸引子的存在性.该随机吸引子是紧不变集并按Lp-范数 吸引L2中所有缓增集，其中，非线性项f满足p-1 （p≥2）阶增长条件.

Abstract

We focus on the asymptotic behavior of solution for reaction-diffusion equation with multiplicative noise on unbounded domains. The uniform estimates is used to obtain the Lp-random absorbing set. A new priori estimate method, called asymptotic priori estimate, is applied to the unbounded part of solution to establish the Lp-asymptotic compactness of the corresponding random dynamical system, then the existence of Lp-random attractor is proved. This random attractor is not only a compact set but an invariant tempered set which attracts every tempered random subset of L2 in the topology of Lp. The nonlinearity term f is allowed to possess some growth of arbitrary order p - 1, where p ≥ 2.

关键词

随机反应扩散方程 / 可乘白噪音 / 渐近优先估计 / Lp-随机吸引子

Key words

stochastic reaction-diffusion equation / multiplicative noise / the asymptotic priori estimates / Lp-random attractor

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刘林芳, 尹福其. 随机反应扩散方程的Lp-随机吸引子. 数学学报, 2014, 57(4): 751-766 https://doi.org/10.12386/A2014sxxb0070
Lin Fang LIU, Fu Qi YIN. Lp-Random Attractor for Stochastic Reaction-Diffusion Equation on Unbounded Domains. Acta Mathematica Sinica, Chinese Series, 2014, 57(4): 751-766 https://doi.org/10.12386/A2014sxxb0070

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基金

国家自然科学基金资助项目（11171280，11101054）湖南省教育厅基金资助项目（12C0408）；湘潭大学博士后基金资助项目

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