# 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…

## 18 Citations

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

- MathematicsSIAM J. Math. Anal.
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This work considers reaction-diffusion equations that are stochastically forced by a small multiplicative noise term and obtains a quasi-linear SPDE that describes the fluctuations from the primary wave by applying a stochastic phase-shift and a time-transform.

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We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations with additive noise. Special attention is given to the effect of small noise on the classical…

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This work considers reaction-diffusion equations that are stochastically forced by a small multiplicative noise term and obtains a quasi-linear SPDE that describes the fluctuations from the primary wave by applying a stochastic phase-shift and a time-transform.

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