Stability of Travelling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations
Analysis of PDEs
2020-06-26 v2
Abstract
In this paper we establish the meta-stability of travelling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in [hamster2017,hamster2020] can be maintained over timescales that are exponentially long with respect to the noise intensity. This is achieved by combining the generic chaining principle with a mild version of the Burkholder-Davis-Gundy inequality to establish logarithmic supremum bounds for stochastic convolutions in the critical regularity regime.
Keywords
Cite
@article{arxiv.2003.02044,
title = {Stability of Travelling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations},
author = {Christian Hamster and Hermen Jan Hupkes},
journal= {arXiv preprint arXiv:2003.02044},
year = {2020}
}