On blowup dynamics in the Keller–Segel model of chemotaxis

Dejak, S.; Egli, D.; Lushnikov, P.; Sigal, I.

doi:10.1090/S1061-0022-2014-01306-4

On blowup dynamics in the Keller–Segel model of chemotaxis
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by S. I. Dejak, D. Egli, P. M. Lushnikov and I. M. Sigal

St. Petersburg Math. J. 25 (2014), 547-574

DOI: https://doi.org/10.1090/S1061-0022-2014-01306-4

Published electronically: June 5, 2014

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Abstract:

The (reduced) Keller–Segel equations modeling chemotaxis of bio-organisms are investigated. A formal derivation and partial rigorous results of the blowup dynamics are presented for solutions of these equations describing the chemotactic aggregation of the organisms. The results are confirmed by numerical simulations, and the formula derived coincides with the formula of Herrero and Velázquez for specially constructed solutions.

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