非线性噪声驱动下随机演化方程的路径不稳定不变流形约简

IF 0.5 4区 数学 Q3 MATHEMATICS
Xuewei Ju
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引用次数: 0

摘要

研究了具有Lipschitz连续漂移项F(u)和Lipschitz连续扩散项G(u)的可分离Hilbert空间H上随机演化方程du + Audt = F(u)dt + G(u)dW(t)的路径动力学。我们首先引入广义随机动力系统(GRDS)的概念,并证明该方程可以生成广义随机动力系统。当漂移项和扩散项的Lipschitz常数满足谱隙条件时,我们构造了GRDS的路径不稳定流形。最后,我们给出了GRDS的路径不稳定流形约简。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Pathwise unstable invariant manifolds reduction for stochastic evolution equations driven by nonlinear noise
This paper is concerned with the pathwise dynamics of the stochastic evolution equation: du + Audt = F(u)dt + G(u)dW(t) on a separable Hilbert space H with the Lipschitz continuous drift term F(u) as well as the Lipschitz continuous diffusion term G(u). We first introduce the notion of generalized random dynamical systems (GRDSs) and show that the equation can generate a GRDS. We then construct a pathwise unstable manifold for the GRDS provided that the Lipschitz constants of the drift term and the diffusion term satisfy a spectral gap condition. At last, we present a pathwise unstable manifold reduction for the GRDS.
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来源期刊
CiteScore
0.70
自引率
20.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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