带奇异项的分数阶反应扩散方程的动力学行为
Dynamics of Fractional Reaction-diffusion Equations with Singular Terms
谢江华 1赵文强1
作者信息
- 1. 重庆工商大学 数学与统计学院,重庆 400067
- 折叠
摘要
考虑定义在光滑有界域 O⊂Rn 上的具有加性噪声和奇异扰动的分数阶非自治随机反应扩散方程在空间L2(O)上的随机吸引子的存在性.奇异项和分数阶拉普拉斯算子的相互作用,导致无法得到解在正则空间上的估计,不能通过 Sobolev紧嵌入获得解在空间 L2(O)上的紧性,故利用 Aubin紧性定理克服了这一困难.
Abstract
The existence of random attractors in space L2(O)for fractional non-autonomous stochastic reaction-diffusion equations with additive noise and singular perturbations defined on smooth bounded domain O⊂Rn is discussed.Because of the interaction between singular term and fractional Laplace operator,the solution cannot be estimated on regular spaces,so the compactness of solution in spaces L2(O)cannot be obtained by Sobolev compact embedding.So Aubin compactness theorem is used to overcome the difficulty.
关键词
奇异扰动/加性噪声/紧性/分数阶算子/吸引子Key words
singular perturbations/additive noise/compactness/fractional operator/attractor引用本文复制引用
基金项目
国家自然科学基金(11871122)
重庆市自然科学基金(CSTC2019JCYJ-MSXMX0115)
出版年
2024
NETL
NSTL
万方数据