2020/03/04 by Christian Hamster, Hamster, Christian, Hermen Jan Hupkes +1
Computer Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2003.02044
openalex publication_date 2020/03/04 · openalex created_date 2020/03/13 · openalex updated_date 2026/07/28
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.