Some transport and diffusion processes on networks and their graph realizability

被引：14
作者：
Banasiak, J. [1 ,2 ]
Falkiewicz, A. [2 ]
机构：
[1] Univ KwaZulu Natal, Sch Math Sci, Durban, South Africa
[2] Lodz Univ Technol, Inst Math, Lodz, Poland
来源：
APPLIED MATHEMATICS LETTERS | 2015年 / 45卷
关键词：
Transport on networks; Diffusion on networks; Graphs; Digraphs; Line graphs; FLOWS;
D O I：
10.1016/j.aml.2015.01.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider systems of transport and diffusion problems on one-dimensional domains coupled through transmission type boundary conditions at the endpoints and determine what types of such problems can be identified with respective problems on metric graphs. For the transport problem the answer is provided by a reformulation of a graph theoretic result characterizing line digraphs of a digraph, whereas in the case of diffusion the answer is provided by an algebraic characterization of matrices which are adjacency matrices of line graphs, which complements known results from graph theory and is particularly suitable for this application. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：25 / 30
页数：6
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