S. I. Dejak, D. Egli, P. M. Lushnikov, I. M. Sigal, “On blowup dynamics in the Keller–Segel model of chemotaxis”, Algebra i Analiz, 2013, Volume 25, Issue 4,Pages <nobr>47

This article is cited in 6 papers

Research Papers

On blowup dynamics in the Keller–Segel model of chemotaxis

S. I. Dejak^a, D. Egli^a, P. M. Lushnikov^b, I. M. Sigal^a

^a University of Toronto, Department of Mathematics, Toronto, Canada
^b University of New Mexico, Department of Mathematics and Statistics, USA

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.

Keywords: reaction-diffusion equations, nonlinear partial differential equations, blowup, collapse, chemotaxis, Keller–Segel equation, blowup profile.

Received: 01.12.2012

Language: English