TY - JOUR

T1 - The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes

AU - Hausenblas, Erika

AU - Mukherjee, Debopriya

AU - Tran, Tuan Hoang

PY - 2022

Y1 - 2022

N2 - 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. .....

AB - 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. .....

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85119506292&partnerID=MN8TOARS

U2 - 10.1016/j.jde.2021.10.056

DO - 10.1016/j.jde.2021.10.056

M3 - Article

VL - 310.2022

SP - 506

EP - 554

JO - Journal of differential equations

JF - Journal of differential equations

SN - 0022-0396

IS - 15 February

ER -