| Issue |
Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016
Anomalous diffusion
|
|
|---|---|---|
| Page(s) | 157 - 178 | |
| DOI | https://doi.org/10.1051/mmnp/201611310 | |
| Published online | 21 June 2016 | |
Proliferating Lévy Walkers and Front Propagation
1 School of Mathematics, The University of Manchester, M13 9 PL Manchester, UK
2 Universitat Autónoma de Barcelona, Departament de Física, Facultat de Ciències. Edifici Cc 08193 - Cerdanyola del Vallès ( Barcelona ) Spain
⋆ Corresponding author. E-mail: sergei.fedotov@manchester.ac.uk
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.
Mathematics Subject Classification: 60G22 / 82C31 / 82C70 / 92B05
Key words: anomalous diffusion
© EDP Sciences, 2016
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