具有非线性彩色噪声的随机准线性方程的回拉随机吸引子的高阶连续性

IF 1.4 4区 数学 Q1 MATHEMATICS
Yangrong Li, Fengling Wang, Tomás Caraballo
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引用次数: 0

摘要

对于非自治随机动力系统,我们引入了回拉随机双空间吸引子(PRBA)的概念。我们证明了 PRBA 的存在定理,其中包括它在规则空间中的可测性、紧凑性和吸引力。然后,我们建立了从参数空间到配备豪斯多夫度量的正则空间所有紧凑子集空间的 PRBA 族的剩余密集连续性。抽象结果在非线性彩色噪声驱动的非自主随机准线性方程中得到了说明,其中噪声的大小属于 \((0,\infty ]\) 而无限大对应于确定性方程。应用结果是在\((0,\infty ]\)上的PRBA在平方和p阶Lebesgue空间(其中\(p>2\))中的存在性和剩余密集连续性。即使对于自主确定性系统,正则空间中吸引子的下半连续性似乎也是一个新课题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Higher-Order Continuity of Pullback Random Attractors for Random Quasilinear Equations with Nonlinear Colored Noise

For a nonautonomous random dynamical system, we introduce a concept of a pullback random bi-spatial attractor (PRBA). We prove an existence theorem of a PRBA, which includes its measurability, compactness and attraction in the regular space. We then establish the residual dense continuity of a family of PRBAs from a parameter space into the space of all compact subsets of the regular space equipped by Hausdorff metric. The abstract results are illustrated in the nonautonomous random quasilinear equation driven by nonlinear colored noise, where the size of noise belongs to \((0,\infty ]\) and the infinite size corresponds to the deterministic equation. The application results are the existence and residual dense continuity of PRBAs on \((0,\infty ]\) in both square and p-order Lebesgue spaces, where \(p>2\). The lower semi-continuity of attractors in the regular space seems to be a new subject even for an autonomous deterministic system.

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来源期刊
CiteScore
3.30
自引率
7.70%
发文量
116
审稿时长
>12 weeks
期刊介绍: Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
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