Nonlinear flux-limited models for chemotaxis on networks

Raul Borsche; Axel Klar; T. N. Ha Pham; Raul Borsche; Axel Klar; T. N. Ha Pham

doi:10.3934/nhm.2017017

Networks and Heterogeneous Media

2017, Volume 12, Issue 3: 381-401. doi: 10.3934/nhm.2017017

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Nonlinear flux-limited models for chemotaxis on networks

Technische Universität Kaiserslautern, Department of Mathematics, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany

Received: 01 September 2016 Revised: 01 May 2017
Primary: 92C17, 92C42; Secondary: 65M06

In this paper we consider macroscopic nonlinear moment models for the approximation of kinetic chemotaxis equations on a network. Coupling conditions at the nodes of the network for these models are derived from the coupling conditions of kinetic equations. The results of the different models are compared and relations to a Keller-Segel model on networks are discussed. For a numerical approximation of the governing equations an asymptotic well-balanced schemes is extended to directed graphs. Kinetic and macroscopic equations are investigated numerically and their solutions are compared for tripod and more general networks.
- Chemotaxis,
- kinetic equation,
- nonlinear maximum entropy,
- moment closure,
- relaxation schemes,
- networks,
- coupling conditions
Citation: Raul Borsche, Axel Klar, T. N. Ha Pham. Nonlinear flux-limited models for chemotaxis on networks[J]. Networks and Heterogeneous Media, 2017, 12(3): 381-401. doi: 10.3934/nhm.2017017

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Abstract

In this paper we consider macroscopic nonlinear moment models for the approximation of kinetic chemotaxis equations on a network. Coupling conditions at the nodes of the network for these models are derived from the coupling conditions of kinetic equations. The results of the different models are compared and relations to a Keller-Segel model on networks are discussed. For a numerical approximation of the governing equations an asymptotic well-balanced schemes is extended to directed graphs. Kinetic and macroscopic equations are investigated numerically and their solutions are compared for tripod and more general networks.

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