Geodesic
Fractional Keller-Segel equations
Salem, Samir1; Lafleche, Laurent1
1CEREMADE UMR 7534 Université Paris Dauphine Place du Maréchal de Tassigny Cedex Paris France
Séminaire Laurent Schwartz — EDP et applications (2018-2019), Talk no. 3, 11 p.

See the original proceeding notice from the Numdam source

This note summarizes some results provided in the papers [14, 17], concerning the study of the fractional Keller-Segel model. This diffusion aggregation equation arises in the modeling of the chemotaxis motion of bacteria. The diffusion part consists in a fractional Laplacian, and the aggregation kernel is up to the Newtonian one. In the case where the aggregation and diffusion are well balanced, we present how this model can be obtained from an interacting particle system. Then we present some results about well-posedness of the model when the diffusion is not overtaken by the aggregation, and finite time blow-up in the opposite case.

Published online:
DOI: 10.5802/slsedp.126

Salem, Samir  1 ; Lafleche, Laurent  1

1 CEREMADE UMR 7534 Université Paris Dauphine Place du Maréchal de Tassigny Cedex Paris France 
Salem, Samir; Lafleche, Laurent. Fractional Keller-Segel equations. Séminaire Laurent Schwartz — EDP et applications (2018-2019), Talk no. 3, 11 p.. doi: 10.5802/slsedp.126
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     title = {Fractional {Keller-Segel} equations},
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     pages = {1--11},
     year = {2018-2019},
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     doi = {10.5802/slsedp.126},
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