Kinetic and related macroscopic models for chemotaxis on networks

被引：9
|
作者：
Borsche, R. [1 ]
Kall, J. [1 ]
Klar, A. [1 ,2 ]
Pham, T. N. H. [1 ]
机构：
[1] Univ Kaiserslautern, Dept Math, POB 3049, D-67653 Kaiserslautern, Germany
[2] Fraunhofer ITWM Kaiserslautern, D-67653 Kaiserslautern, Germany
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2016年 / 26卷 / 06期
关键词：
Chemotaxis models; kinetic equation; Cattaneo equation; Keller-Segel equation; moment closure; macroscopic limits; relaxation schemes; coupling conditions; KELLER-SEGEL MODEL; CHEMOSENSITIVE MOVEMENT; DIFFUSIVE RELAXATION; HYPERBOLIC MODELS; BLOW-UP; SCHEMES; SYSTEMS; AGGREGATION; INSTABILITY; EQUATIONS;
D O I：
10.1142/S0218202516500299
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1219 / 1242
页数：24
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