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.

32 pages, will appear in St.Petersburg Math Journal (issue dedicated to V.S. Buslaev)

References in corpus (2)

• Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
• Critical dynamics of self-gravitating Langevin particles and bacterial populations