The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes

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  • UNSW

Abstract

Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infection sites. Mathematically chemotaxis is described by the Patlak–Keller–Segel model. This macroscopic system of equations is derived from the microscopic model when limiting behaviour is studied. However, on taking the limit and passing from the microscopic equations to the macroscopic equations, fluctuations are neglected. Perturbing the system by a Gaussian random field restitutes the inherent randomness of the system. This gives us the motivation to study the classical Patlak–Keller–Segel system perturbed by random processes. .....

Details

Original languageUndefined/Unknown
Pages (from-to)506-554
Number of pages49
Journal Journal of differential equations
Volume310.2022
Issue number15 February
Early online date18 Nov 2021
DOIs
Publication statusPublished - 2022