Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise
Analysis of PDEs
2020-03-09 v4
Abstract
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 nonlinear stability question in a fashion that is closely related to modern deterministic methods.
Keywords
Cite
@article{arxiv.1712.00266,
title = {Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise},
author = {C. H. S. Hamster and H. J. Hupkes},
journal= {arXiv preprint arXiv:1712.00266},
year = {2020}
}