Effect of stochastic perturbations for front propagation in Kolmogorov Petrovskii Piscunov equations

John M. Noble

Stochastic Processes and their Applications, 2018, vol. 128, issue 10, 3531-3557

Abstract: This article considers equations of Kolmogorov Petrovskii Piscunov type in one space dimension, with stochastic perturbation: ∂tu=κ2uxx+u(1−u)dt+ϵu∂tζu0(x)=1(−∞,−1Nlog2)(x)+12e−Nx1[−1Nlog2,+∞)(x)where the stochastic differential is taken in the sense of Itô and ζ is a Gaussian random field satisfying Eζ=0 and Eζ(s,x)ζ(t,y)=(s∧t)Γ(x−y). Two situations are considered: firstly, ζ is simply a standard Wiener process (i.e. Γ≡1): secondly, Γ∈C∞(R) with lim|z|→+∞|Γ(z)|=0.

Keywords: Stochastic partial differential equations; Random travelling fronts (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.11.009

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