SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1386-1426, January 2020.
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 quasi-linear stochastic partial differential equation that describes the fluctuations from the primary wave. We subsequently follow the semigroup approach developed in [C. H. S. Hamster and H. J. Hupkes, SIAM J. Appl. Dynam. Syst., 18 (2019), pp. 205--278] to handle the nonlinear stability question. The main novel feature is that we no longer require the diffusion coefficients to be equal.

中文翻译：

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具有乘性噪声的反应扩散方程组的行波稳定性

SIAM数学分析杂志，第52卷，第2期，第1386-1426页，2020年1月。
我们考虑由一个小的乘法噪声项随机强迫的反应扩散方程。我们表明，如果噪声的幅度足够小，则确定性系统的频谱稳定行波解将保留其轨道稳定性。通过将随机相移与时间变换一起应用，我们获得了描述线性波动的准线性随机偏微分方程。随后，我们遵循在[CHS Hamster和HJ Hupkes，SIAM J. Appl。Dynam。Syst。，18（2019），pp.205--278]处理非线性稳定性问题。主要的新颖特征是我们不再要求扩散系数相等。