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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On blowup dynamics in the Keller-Segel model of chemotaxis


Authors: S. I. Dejak, D. Egli, P. M. Lushnikov and I. M. Sigal
Original publication: Algebra i Analiz, tom 25 (2013), nomer 4.
Journal: St. Petersburg Math. J. 25 (2014), 547-574
MSC (2010): Primary 35K51, 35K57, 35Q84, 35Q92
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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Additional Information

S. I. Dejak
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada
Email: steven.dejak@gmail.com

D. Egli
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada
Email: daniel.egli2@gmail.com

P. M. Lushnikov
Affiliation: Department of Mathematics and Statistics, University of New Mexico
Email: plushnik@math.unm.edu

I. M. Sigal
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada
Email: im.sigal@utoronto.ca

DOI: http://dx.doi.org/10.1090/S1061-0022-2014-01306-4
PII: S 1061-0022(2014)01306-4
Keywords: Reaction-diffusion equations, nonlinear partial differential equations, blowup, collapse, chemotaxis, Keller--Segel equation, blowup profile
Received by editor(s): December 1, 2012
Published electronically: June 5, 2014
Additional Notes: The research of the second and fourth authors was partially supported by NSERC under Grant NA7901, and of the third author, by NSF under Grants DMS 0719895 and DMS 0807131
Dedicated: In memory of V. S. Buslaev, a scientist and a friend
Article copyright: © Copyright 2014 American Mathematical Society