Travelling waves for reaction-diffusion equations forced by translation invariant noise

PHYSICA D-NONLINEAR PHENOMENA

卷:401

Article

Hamster, C. H. S.¹  Hupkes, H. J.¹ 

[1] Leiden Univ, Math Inst, POB 9512, NL-2300 RA Leiden, Netherlands

关键词: Travelling waves;    Stochastic forcing;    Nonlinear stability;    Stochastic phase shift;   

DOI  :  10.1016/j.physd.2019.132233

来源: Elsevier

【 摘 要 】

Inspired by applications, we consider reaction-diffusion equations on R that are stochastically forced by a small multiplicative noise term that is white in time, coloured in space and invariant under translations. We show how these equations can be understood as a stochastic partial differential equation (SPDE) forced by a cylindrical Q-Wiener process and subsequently explain how to study stochastic travelling waves in this setting. In particular, we generalize the phase tracking framework that was developed in Hamster and Hupkes (2018,2019) for noise processes driven by a single Brownian motion. The main focus lies on explaining how this framework naturally leads to long term approximations for the stochastic wave profile and speed. We illustrate our approach by two fully worked-out examples, which highlight the predictive power of our expansions. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free