The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Lévy distribution. This article clarifies the form of biologically relevant model equations. We derive Patlak–Keller–Segel-like equations involving nonlocal, fractional Laplacians from a microscopic model for cell movement. Starting from a power-law distribution of run times, we derive a kinetic equation in which the collision term takes into account the long range behavior of the individuals. A fractional chemotactic equation is obtained in a biologically relevant regime. Apart from chemotaxis, our work has implications for biological diffusion in numerous processes.
Fractional Patlak–Keller–Segel equations for chemotactic superdiffusion* / Estrada-Rodriguez, G.; Gimperlein, H.; Painter, K. J.. - In: SIAM JOURNAL ON APPLIED MATHEMATICS. - ISSN 0036-1399. - 78:2(2018), pp. 1155-1173. [10.1137/17M1142867]
|Titolo:||Fractional Patlak–Keller–Segel equations for chemotactic superdiffusion*|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1137/17M1142867|
|Appare nelle tipologie:||1.1 Articolo in rivista|