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 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 language | English |
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Pages (from-to) | 1155-1173 |
Number of pages | 19 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 78 |
Issue number | 2 |
DOIs | |
Publication status | Published - 10 Apr 2018 |
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Profiles
-
Heiko Gimperlein
- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Mathematics - Associate Professor
Person: Academic (Research & Teaching)