Continuous-time random walks and travelling fronts

Fedotov, Sergei and Mèndez, Vicenç (2002) Continuous-time random walks and travelling fronts. Physical Review E, 66. 030102. ISSN 1539-3755

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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.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 82 Statistical mechanics, structure of matter
Depositing User:	Ms Lucy van Russelt
Date Deposited:	19 Jul 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/395

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