2013/10/31 by Jonathan Zinsl, Daniel Matthes
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Chemotaxis #Convergence (economics) #Coupling (piping) #Dependency (UML) #Exponential function #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear system #Population #Population model #math.AP #msc:35A15 #msc:35B40 #msc:35D30 #msc:35K45 #msc:35Q92
paper · pdf · doi:10.2140/apde.2015.8.425
published as Analysis & PDE 8-2 (2015), 425-466 · Improved results: nonlinearity also comprises classical Keller-Segel model; moreover: references added, typos corrected
arxiv created 2014/05/12 · openalex publication_date 2015/05/10 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis; i.e., it models the behavior of a population of bacteria that interact by means of a signaling substance. We assume an external confinement for the bacteria and a nonlinear dependency of the chemotactic drift on the signaling substance concentration.