Stochastic particle approximation for measure valued solutions of the 2D Keller-Segel system

Jan Haskovec*, Christian Schmeiser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

We construct an approximation to the measure valued, global in time solutions to the (Patlak-)Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichotomy in the qualitative behavior of the system and, moreover, captures the solution even after the (possible) blow-up events. We present a numerical method based on this approach and show some numerical results. Moreover, we make a first step toward the convergence analysis of our scheme by proving the convergence of the stochastic particle approximation for the Keller-Segel model with a regularized interaction potential. The proof is based on a BBGKY-like approach for the corresponding particle distribution function.

Original languageEnglish (US)
Pages (from-to)133-151
Number of pages19
JournalJournal of Statistical Physics
Volume135
Issue number1
DOIs
StatePublished - Apr 1 2009

Keywords

  • (Patlak-)Keller-Segel model
  • BBGKY hierarchy
  • Blow-up
  • Chemotaxis
  • Stochastic interacting particles

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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