Proliferating Lévy Walkers and Front Propagation

H. Stage, S. Fedotov, V. Méndez

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

© 2016 EDP Sciences. We develop non-linear integro-differential kinetic equations for proliferating Lévy walkers with birth and death processes. A hyperbolic scaling is applied directly to the general equations to get the Hamilton-Jacobi equations that will allow to determine the rate of front propagation. We found the conditions for switching, birth and death rates under which the propagation velocity reaches the maximum value, i.e. the walker's speed. In the strong anomalous case the death rate was found to influence the velocity of propagation to fall below the walker's maximum speed.
Original languageEnglish
Pages (from-to)157-178
JournalMathematical Modelling of Natural Phenomena
Volume11
Issue number3
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Anomalous diffusion

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