THE SCALAR KELLER–SEGEL MODEL ON NETWORKS-Reference-Cited by-同舟云学术

THE SCALAR KELLER–SEGEL MODEL ON NETWORKS

Published:2013-12-12 Issue:02 Volume:24 Page:221-247
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,GÖTTLICH S.²,KLAR A.¹,SCHILLEN P.²

Affiliation:

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

2. School of Business Informatics and Mathematics, University of Mannheim, 68131 Mannheim, Germany

Abstract

In this work, we extend the one-dimensional Keller–Segel model for chemotaxis to general network topologies. We define appropriate coupling conditions ensuring the conservation of mass and show the existence and uniqueness of the solution. For our computational studies, we use a positive preserving first-order scheme satisfying a network CFL condition. Finally, we numerically validate the Keller–Segel network model and present results regarding special network geometries.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202513400071

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