Conjugate dynamics on center-manifolds for stochastic partial differential equations

被引:8
作者
Zhao, Junyilang [1 ]
Shen, Jun [2 ]
Lu, Kening [3 ]
机构
[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Sichuan, Peoples R China
[2] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China
[3] Brigham Young Univ, Dept Math, Provo, UT 84602 USA
基金
美国国家科学基金会;
关键词
Random dynamical systems; Invariant manifolds; Invariant foliations; Conjugacy between center manifolds; WONG-ZAKAI APPROXIMATIONS; INVARIANT-MANIFOLDS; EVOLUTION EQUATIONS; ASYMPTOTIC STABILITY; CHAOTIC BEHAVIOR; THEOREM; FOLIATIONS; DRIVEN; CONVERGENCE; INTEGRALS;
D O I
10.1016/j.jde.2020.04.032
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we prove that for a random differential equation with the driving noise constructed from a Q-Wiener process and the Wiener shift, there exists a local center, unstable, stable, center-unstable, center - stable manifold, and a local stable foliation, an unstable foliation on the center-unstable manifold, and a stable foliation on the center-stable manifold, the smoothness of which depend on the vector fields of the equation. Also we show that any two arbitrarily local center manifolds constructed as above are conjugate. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码:5997 / 6054
页数:58
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