The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

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...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 31; no. 1; p. 6
Main Authors Huang, Hui, Qiu, Jinniao
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2021
Springer Nature B.V
Subjects
Analysis
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Propagation of chaos
60H30
Bessel potential
Stochastic partial differential equation
Chemotaxis
65M75
35K55
60J7
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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Communicated by Eliot Fried.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-020-09661-6