Stability of Traveling Waves for Reaction-Diffusion Equations with Multiplicative Noise

@article{Hamster2017StabilityOT,
  title={Stability of Traveling Waves for Reaction-Diffusion Equations with Multiplicative Noise},
  author={C. H. S. Hamster and Hermen Jan Hupkes},
  journal={SIAM J. Appl. Dyn. Syst.},
  year={2017},
  volume={18},
  pages={205-278}
}
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling 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 sPDE that describes the fluctuations from the primary wave. We subsequently develop a semigroup approach to handle the… 
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18 Citations

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