Fractional Patlak--Keller--Segel equations for chemotactic superdiffusion
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hdl:2117/374482
Tipus de documentArticle
Data publicació2018-01
EditorSociety for Industrial and Applied Mathematics (SIAM)
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
Abstract
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
CitacióEstrada, G.; Gimperlein, H.; Painter, K. Fractional Patlak--Keller--Segel equations for chemotactic superdiffusion. "SIAM journal on applied mathematics", 2018, vol. 78, núm. 2, p. 1155-1173.
ISSN0036-1399
Versió de l'editorhttps://epubs.siam.org/doi/10.1137/17M1142867
Altres identificadorshttps://arxiv.org/abs/1708.02751
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