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Kinetic and related macroscopic models for chemotaxis on networks

Axel Klar (TU Kaiserslautern)

Abstract: We discuss kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic prob- lem are presented and used to derive coupling conditions for the macroscopic approximations. The results of the different models are compared and relations to a Keller-Segel model on networks are discussed. For a numerical approxima- tion of the governing equations asymptotic preserving relaxation schemes are extended to directed graphs. Kinetic and macroscopic equations are investi- gated numerically and their solutions are compared for tripod and more general networks. Coupling of network problem with 2D equations is discussed as well.
Joint work with: Raul Borsche, (TU Kaiserslautern), Simone Göttlich (U Mannheim), T.N.Ha Pham (TU Kaiserslautern), P.Schillen (U Mannheim).

[1] R. Borsche, A. Klar, and T.N.H. Pham, ar, T.N.H. Pham, Kinetic and re- lated macroscopic models for chemotaxis on networks, to appear in M3AS, (2016).
[2] R. Borsche, S. Göttlich, A. Klar, and P. Schillen, The Keller-Segel model on networks, M3AS, (2014), pp. 221-247.
[3] R. Borsche, A. Klar, S. Kühn, A. Meurer, Coupling traffic flow networks to pedestrian and crowd motion, M3AS, (2014), pp. 359-380.
[4] R. Borsche, A. Klar, Flooding in urban drainage systems: coupling hyperbolic conservation laws for sewer systems and surface flow, Int. J. Num. Meth. Fluids, 76 (2014), pp. 789-810.