期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 248, 期 7, 页码 1637-1667出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2009.11.006
关键词
Stochastic PDEs; Fractional Brownian motion; Random dynamical systems; Invariant manifolds
类别
资金
- Ministerio de Ciencia e Innovacion [MTM2005-01412, MTM2008-00088]
- Junta de Andalucia [P07-FQM-02468]
- [NSF0401708]
- [NSFC10371083]
- [DFG17355596]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0909400] Funding Source: National Science Foundation
In this paper, we consider a class of stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion (fBm) with the Hurst parameter bigger than 1/2. The existence of local random unstable manifolds is shown if the linear parts of these SPDEs are hyperbolic. For this purpose we introduce a modified Lyapunov-Perron transform, which contains stochastic integrals. By the singularities inside these integrals we obtain a special Lyapunov-Perron's approach by treating a segment of the solution over time interval [0,1] as a starting point and setting up an infinite series equation involving these segments as time evolves. Using this approach, we establish the existence of local random unstable manifolds in a tempered neighborhood of an equilibrium. (C) 2009 Elsevier Inc. All rights reserved.
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