Stability of travelling waves in stochastic bistable reaction-diffusion equations

Wilhelm Stannat

Stability of travelling waves in stochastic bistable reaction-diffusion equations

Probability 2014-05-01 v2 Analysis of PDEs Dynamical Systems

Authors: Wilhelm Stannat

Abstract

We extend the result on the stability of travelling waves for stochastic Nagumo equations in [St] to general bistable reaction-diffusion equations with both additive and multiplicative noise, using a variational approach based on functional inequalities. Our analysis yields explicit estimates on the rate of stability that can be shown in special examples to be optimal. [St] Stannat, W., Stability of travelling waves in stochastic Nagumo equations, arXiv:1301.6378, 2013.

Keywords

travelling waves stability stochastic bistable reaction-diffusion equations variational approach nagumo equation additive noise multiplicative noise

Cite

@article{arxiv.1404.3853,
  title  = {Stability of travelling waves in stochastic bistable reaction-diffusion equations},
  author = {Wilhelm Stannat},
  journal= {arXiv preprint arXiv:1404.3853},
  year   = {2014}
}