一类非自治分数阶随机波动方程的随机吸引子

文慧霞, 舒级, 李林芳

数学学报 ›› 2019, Vol. 62 ›› Issue (1) : 25-40.

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数学学报 ›› 2019, Vol. 62 ›› Issue (1) : 25-40. DOI: 10.12386/A2019sxxb0003
论文

一类非自治分数阶随机波动方程的随机吸引子

    文慧霞, 舒级, 李林芳
作者信息 +

The Random Attractors for a Class of Nonautonomous Fractional Stochastic Wave Equations

    Hui Xia WEN, Ji SHU, Lin Fang LI
Author information +
文章历史 +

摘要

本文考虑带加性噪声的非自治分数阶随机波动方程在无界区域Rn上的渐近行为.首先将随机偏微分方程转化为随机方程,其解产生一个随机动力系统,然后运用分解技术建立该系统的渐近紧性,最后证明随机吸引子的存在性.

Abstract

We consider the asymptotic behavior of non-autonomous stochastic fractional wave equations on an unbounded domain Rn. We firstly transform the equation into a random equation whose solutions generate a random one system. Then we establish the asymptotical compactness of the system by the splitting technique. Finally the existence of random attractors is proved.

关键词

非自治分数阶随机波动方程 / 随机动力系统 / 随机吸引子 / 分解技术 / 加性噪声

Key words

non-autonomous stochastic fractional wave equation / random dynamical system / random attractor / the splitting technique / additive noise

引用本文

导出引用
文慧霞, 舒级, 李林芳. 一类非自治分数阶随机波动方程的随机吸引子. 数学学报, 2019, 62(1): 25-40 https://doi.org/10.12386/A2019sxxb0003
Hui Xia WEN, Ji SHU, Lin Fang LI. The Random Attractors for a Class of Nonautonomous Fractional Stochastic Wave Equations. Acta Mathematica Sinica, Chinese Series, 2019, 62(1): 25-40 https://doi.org/10.12386/A2019sxxb0003

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基金

国家自然科学基金资助项目(11371267,11571245);四川省科技厅应用基础计划项目(2016JY0204)

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