The microscopic derivation and well-posedness of the stochastic Keller-Segel equation

2019/08/09 by Hui Huang, Huang, Hui, Jinniao Qiu +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1908.03375

openalex publication_date 2019/08/09 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose and study a stochastic aggregation-diffusion equation of the Keller-Segel (KS) type for modeling the chemotaxis in dimensions d=2,3. Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

Citations

• On explosions of solutions to a system of partial differential equations modelling chemotaxis
• A user’s guide to PDE models for chemotaxis

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• Quantitative approximation of a Keller--Segel PDE by a branching moderately interacting particle system and suppression of blow-up
• Microscopic derivation of the Keller-Segel equation in the sub-critical regime
• The 2-D stochastic Keller-Segel particle model : existence and uniqueness
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