期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 18, 期 1, 页码 205-278出版社
SIAM PUBLICATIONS
DOI: 10.1137/17M1159518
关键词
traveling waves; stochastic forcing; nonlinear stability; stochastic phase shift
资金
- Netherlands Organization for Scientific Research (NWO) [639.032.612]
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the amplitude of the noise is sufficiently small. By applying a stochastic phase shift together with a time transform, we obtain a semilinear Stochastic partial differential equation that describes the fluctuations from the primary wave. We subsequently develop a semigroup approach to handle the nonlinear stability question in a fashion that is closely related to modern deterministic methods.
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