TITLE

Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System

AUTHOR(S)
Haškovec, Jan; Schmeiser, Christian
PUB. DATE
April 2009
SOURCE
Journal of Statistical Physics;Apr2009, Vol. 135 Issue 1, p133
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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.
ACCESSION #
37826456

 

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