Applied Analysis

Seminar information archive ~05/22Next seminarFuture seminars 05/23~

Date, time & place Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.)

2008/11/20

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jan Haskovec
(Vienna University of Technology(オーストリア))
Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System
[ Abstract ]
We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichtomy 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.