Continuous-time random walks and traveling fronts

Sergei Fedotov, Vicenç Méndez

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher-Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processes. ©2002 The American Physical Society.
    Original languageEnglish
    Article number030102
    Pages (from-to)030102/4
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume66
    Issue number3
    DOIs
    Publication statusPublished - Sept 2002

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