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

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, mo...

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Bibliographic Details
Published in:Journal of statistical physics 2009-04, Vol.135 (1), p.133-151
Main Authors: Haškovec, Jan, Schmeiser, Christian
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-009-9717-1