Travelling waves for discrete stochastic bistable equations
OPEN ACCESS
Loading...
Author / Producer
Date
2024
Publication Type
Journal Article
ETH Bibliography
yes
Citations
Altmetric
OPEN ACCESS
Data
Rights / License
Abstract
Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise. In this paper we study the combined effect of spatial discretization and stochastic perturbations on travelling waves in the Nagumo equation, which is a prototypical model for bistable reaction-diffusion partial differential equations (PDEs). We prove that under suitable parameter conditions, various discrete-stochastic variants of the Nagumo equation have solutions, which stay close on long time scales to the classical monotone Nagumo front with high probability if the noise covariance and spatial discretization are sufficiently small.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
5 (6)
Pages / Article No.
35
Publisher
Springer
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Nagumo equation; Bistability; Stochastic partial differential equation; Lattice differential equation; Travelling wave; Noise; Discretization; Allen-Cahn equation; Ginzburg-Landau equation; Φ4 model; Schlögl equation