Kinetic and related macroscopic models for chemotaxis on networks-Reference-Cited by-同舟云学术

Kinetic and related macroscopic models for chemotaxis on networks

Published:2016-04-12 Issue:06 Volume:26 Page:1219-1242
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Borsche R.¹,Kall J.¹,Klar A.¹²,Pham T. N. H.¹

Affiliation:

1. Department of Mathematics, University of Kaiserslautern, P. O. Box 3049, 67653 Kaiserslautern, Germany

2. Fraunhofer ITWM Kaiserslautern, 67653 Kaiserslautern, Germany

Abstract

In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem 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 approximation of the governing equations asymptotic preserving relaxation schemes are extended to directed graphs. Kinetic and macroscopic equations are investigated numerically and their solutions are compared for tripod and more general networks.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202516500299

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