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arXiv · 2003.02044

Stability of Travelling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations

Christian Hamster·Hermen Jan Hupkes
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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.

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Christian Hamster, Hermen Jan Hupkes. 2020-03-04. Stability of Travelling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations. https://arxiv.org/abs/2003.02044

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