Some transport and diffusion processes on networks and their graph realizability. (July 2015)

• Record Type: Journal Article
• Authors: Banasiak, J.; Falkiewicz, A.
• Is Part Of: Applied mathematics letters. Volume 45(2015:Jul.)
• Page Start: 25
• Page End: 30
• Publication Date: 2015-07
• Subjects: Transport on networks -- Diffusion on networks -- Graphs -- Digraphs -- Line graphs; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.01.006
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.