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Particle approximation of the $2$-$d$ parabolic-elliptic Keller-Segel system in the subcritical regime

Abstract : The parabolic-elliptic Keller-Segel partial differential equation is a two-dimensional model for chemotaxis. In this work we introduce a stochastic system of moderately interacting particles which converges, globally in time, to the solution to the Keller-Segel model in $2$-d. The advantage of our approach is that we show the convergence in a strong sense for all the subcritical values of the total mass, $M < 8\pi$.
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https://hal.inria.fr/hal-02537226
Contributor : Milica Tomasevic <>
Submitted on : Wednesday, April 8, 2020 - 5:05:04 PM
Last modification on : Sunday, November 29, 2020 - 6:48:02 PM

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  • HAL Id : hal-02537226, version 1
  • ARXIV : 2004.03177

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Christian Olivera, Alexandre Richard, Milica Tomasevic. Particle approximation of the $2$-$d$ parabolic-elliptic Keller-Segel system in the subcritical regime. 2020. ⟨hal-02537226⟩

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