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Continuous-time random walks and traveling fronts

Sergei Fedotov and Vicenç Méndez
Phys. Rev. E 66, 030102(R) – Published 18 September 2002
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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.

  • Received 6 May 2002

DOI:https://doi.org/10.1103/PhysRevE.66.030102

©2002 American Physical Society

Authors & Affiliations

Sergei Fedotov1 and Vicenç Méndez2

  • 1Department of Mathematics, UMIST — University of Manchester Institute Science and Technology, Manchester M60 1QD, United Kingdom
  • 2Departament de Medicina, Universitat Internacional de Catalunya, c./Gomera s/n, 08190-Sant Cugat del Vallès, Barcelona, Spain

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Vol. 66, Iss. 3 — September 2002

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