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. .....
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Original language | Undefined/Unknown |
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Pages (from-to) | 506-554 |
Number of pages | 49 |
Journal | Journal of differential equations |
Volume | 310.2022 |
Issue number | 15 February |
Early online date | 18 Nov 2021 |
DOIs | |
Publication status | Published - 2022 |