Fractional Patlak-Keller-Segel Equations for Chemotactic Superdiffusion

@article{EstradaRodriguez2017FractionalPE,
  title={Fractional Patlak-Keller-Segel Equations for Chemotactic Superdiffusion},
  author={Gissell Estrada-Rodriguez and Heiko Gimperlein and Kevin J. Painter},
  journal={SIAM J. Appl. Math.},
  year={2017},
  volume={78},
  pages={1155-1173}
}
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… 
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