The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes
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In: Journal of differential equations, Vol. 310.2022, No. 15 February, 2022, p. 506-554.
Research output: Contribution to journal › Article › Research › peer-review
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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 -