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

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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.

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Authors and Affiliations

  1. Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria

    Jan Haškovec

  2. Faculty of Mathematics, University of Vienna, Vienna, Austria

    Christian Schmeiser

  3. RICAM, Linz, Austria

    Christian Schmeiser

Authors
  1. Jan Haškovec
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  2. Christian Schmeiser
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Correspondence to Jan Haškovec.

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Haškovec, J., Schmeiser, C. Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System. J Stat Phys 135, 133–151 (2009). https://doi.org/10.1007/s10955-009-9717-1

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  • DOI: https://doi.org/10.1007/s10955-009-9717-1

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