Model Hierarchies for Cell Aggregation by Chemotaxis
نویسندگان
چکیده
We present PDE (partial differential equation) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. Also we derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finite-time blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of Leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed. Chemotaxis, Keller-Segel model, Moment expansion, Macroscopic limit. AMS Subject Classification: 92C17
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