The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation
Hui Huang, Jinniao Qiu
Abstract
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 $$d=2,3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . 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.
Topics & Concepts
Limit (mathematics)DiffusionField (mathematics)AlgorithmComputer scienceMathematicsMathematical analysisPhysicsThermodynamicsPure mathematicsMathematical Biology Tumor GrowthGene Regulatory Network AnalysisAdvanced Mathematical Modeling in Engineering