On blowup dynamics in the Keller-Segel model of chemotaxis
Abstract
We investigate the (reduced) Keller-Segel equations modeling chemotaxis of bio-organisms. We present a formal derivation and partial rigorous results of the blowup dynamics of solution of these equations describing the chemotactic aggregation of the organisms. Our results are confirmed by numerical simulations and the formula we derive coincides with the formula of Herrero and Velázquez for specially constructed solutions.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2013
- DOI:
- 10.48550/arXiv.1304.1583
- arXiv:
- arXiv:1304.1583
- Bibcode:
- 2013arXiv1304.1583D
- Keywords:
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- Nonlinear Sciences - Pattern Formation and Solitons;
- Mathematical Physics;
- Mathematics - Analysis of PDEs;
- Physics - Biological Physics
- E-Print:
- 32 pages, will appear in St.Petersburg Math Journal (issue dedicated to V.S. Buslaev)