带有强阻尼的粘弹性方程的随机吸引子
Random Attractors of Viscoelastic Equation with Strong Damping
DOI: 10.12677/PM.2022.1210174, PDF,   
作者: 任玉晶, 马文君, 马巧珍*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 随机吸引子；粘弹性方程；渐近紧性；Random Attractors； Viscoelastic Equation； Asymptotic Compactness
摘要: 关于有界域上的粘弹性问题已经被很多人研究，但目前还未见无界域上的相关研究，所以本文将考虑无界域上具有加性噪声的粘弹性方程解的渐近行为。为了克服在无界域上由Sobolev嵌入的非紧性所造成的困难，我们利用截断函数和算子分解的方法，得到了解的渐近紧性，最后，获得了与方程相关的动力系统随机吸引子的存在唯一性。
Abstract: The viscoelastic problem in bounded domain has been studied by many authors, but there is no relevant study in unbounded domain. Therefore, in this paper, the asymptotic behavior of the so-lution of viscoelastic equation with additive noise in unbounded domain is considered. To overcome the difficulty caused by the noncompactness of Sobolev embeddedness on unbounded domains, a cut-off function and a decomposition trick are used to establish the asymptotic compactness of the solutions. Finally, we obtain the existence and uniqueness of random attractors for dynamical systems associated with the equation.
文章引用：任玉晶, 马文君, 马巧珍. 带有强阻尼的粘弹性方程的随机吸引子[J]. 理论数学, 2022, 12(10): 1597-1614. https://doi.org/10.12677/PM.2022.1210174

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