An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena-Reference-Cited by-同舟云学术

An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

Published:2018-12-01 Issue:2 Volume:9 Page:61-75
ISSN:2038-0909
Container-title:Communications in Applied and Industrial Mathematics
language:en
Short-container-title:

Author:

Bellouquid Abdelghani¹,Tagoudjeu Jacques²

Affiliation:

1. Cadi Ayyad University, ENSA Marrakech , Morocco

2. University of Yaounde I, Ecole Nationale Superieure Polytechnique and CETIC-ACE, Yaounde , Cameroon

Abstract

Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Industrial and Manufacturing Engineering

Link

https://www.sciendo.com/pdf/10.2478/caim-2018-0010

Reference41 articles.

1. 1. C.S. Patlak, Random walk with persistence and external bias, Bull. Math. Biol. Biophys., vol. 15, pp. 311-338, 1953.

2. 2. E.F. Keller and L.A. Segel, Traveling band of chemotactic bacteria: A theoretical analysis, J. Theor. Biol., vol. 30, pp. 235-248, 1971.

3. 3. T. Hillen and K.J. Painter, A users guide to PDE models for chemotaxis, J. Math. Biol., vol. 58 pp. 183-217, 2009.

4. 4. D. Horstmann, From 1970 until present: The Keller{Segel model in chemotaxis and its consequences. I, Jahresberichte Deutsch. Math.-Verein, vol. 105, pp. 103-165, 2003.

5. 5. N. Bellomo, A. Bellouquid, Y. Tao, and M. Winkler, Toward a mathematical theory of Keller-Segelmodels of pattern formation in biological tissues, Math. Models Methods Appl. Sci. , vol. 25, no. 09, pp. 1663-1763, 2015.

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