| 吴 苑，乔 丹，李晓军*.无界域上带非线性阻尼和强阻尼随机波动
方程解的性态[J].海南师范大学学报自科版,2021,34(3):245-255 |
| 无界域上带非线性阻尼和强阻尼随机波动
方程解的性态 |
| The Behavior of Solutions to Stochastic Wave Equations withNonlinear Damping and Strong Damping on Unbounded Domains |
| |
| DOI：10.12051/j.issn.1674-4942.2021.03.001 |
| 中文关键词: 强阻尼 波动方程 随机吸引子 渐近紧性 无界域 |
| 英文关键词: strong damping wave equations random attractor asymptotic compactness unbounded domain |
| 基金项目:国家自然科学基金项目（11571092） |
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| 摘要点击次数: 489 |
| 全文下载次数: 305 |
| 中文摘要: |
| 本文研究无界域上带非线性阻尼、强阻尼以及可加噪声的非自治随机波动方程随机吸
引子的存在性。首先证明该方程组的解可以定义一个随机动力系统，然后对方程的解进行一致估
计得到此随机动力系统 D -拉回随机吸收集的存在性，最后利用空间分割的方法克服无界域上
Sobolev嵌入缺乏紧性的困难并证得此随机动力系统的D -拉回渐近紧性，进而得到该动力系统随
机吸引子的存在性。 |
| 英文摘要: |
| This article investigated the existence of random attractor for non-autonomous stochastic wave equation with
nonlinear damping term and strong damping term, as well as additive noise on the unbounded domain. Firstly, it was proved
that the solution of the equation can generate a random dynamical system, and then the uniform estimation of the solution
was given to get the existence of D -pullback random absorbing set of the random dynamical system. Finally, the method of
space division was used to overcome the non-compactness of Sobolev embedding on the unbounded domain and get the
D -pullback asymptotical compactness of the random dynamical system, and then the existence of the random attractor of
the dynamic system was obtained. |
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