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On blowup dynamics in the Keller-Segel model of chemotaxis. (English) Zbl 1326.35049

St. Petersbg. Math. J. 25, No. 4, 547-574 (2014) and Algebra Anal. 25, No. 4, 47-84 (2013).
Summary: 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 M. A. Herrero and J. J. L. Velázquez [J. Math. Biol. 35, No. 2, 177–194 (1996; Zbl 0866.92009)] for specially constructed solutions.

MSC:

35B44 Blow-up in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35Q84 Fokker-Planck equations
92C17 Cell movement (chemotaxis, etc.)

Citations:

Zbl 0866.92009
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References:

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