Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion

Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
60 Downloads (Pure)


The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy 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 behaviour 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.
Original languageEnglish
Pages (from-to)1155-1173
Number of pages19
JournalSIAM Journal on Applied Mathematics
Issue number2
Publication statusPublished - 10 Apr 2018


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