ANALYSIS OF A SYSTEM OF NONLOCAL CONSERVATION LAWS FOR MULTI-COMMODITY FLOW ON NETWORKS
Gugat M, Keimer A, Leugering G, Wang Z (2015)
Publication Status: Published
Publication Type: Journal article
Publication year: 2015
Journal
Publisher: American Institute of Mathematical Sciences (AIMS)
Book Volume: 10
Pages Range: 749-785
Journal Issue: 4
Abstract
We consider a system of scalar nonlocal conservation laws on networks that model a highly re-entrant multi-commodity manufacturing system as encountered in semi-conductor production. Every single commodity is modeled by a nonlocal conservation law, and the corresponding PDEs are coupled via a collective load, the work m progress. We illustrate the dynamics for two commodities. In the applications, directed acyclic networks naturally occur, therefore this type of networks is considered. On every edge of the network we have a system of coupled conservation laws with nonlocal velocity. At the junctions the right hand side boundary data of the foregoing edges is passed as left hand side boundary data to the following edges and PDEs. For distributing junctions, where we have more than one outgoing edge, we impose time dependent distribution functions that guarantee conservation of mass. We provide results of regularity, existence and well-posedness of the multicommodity network model for L-P-, BV- and W-1,W-p-data. Moreover, we define an L-2-tracking type objective and show the existence of minimizers that solve the corresponding optimal control problem.
Authors with CRIS profile
Martin Gugat
Lehrstuhl für Angewandte Mathematik
Alexander Keimer
Lehrstuhl für Angewandte Mathematik
Günter Leugering
Lehrstuhl für Angewandte Mathematik
Involved external institutions
China (CN)How to cite
APA:
Gugat, M., Keimer, A., Leugering, G., & Wang, Z. (2015). ANALYSIS OF A SYSTEM OF NONLOCAL CONSERVATION LAWS FOR MULTI-COMMODITY FLOW ON NETWORKS. Networks and Heterogeneous Media, 10(4), 749-785. https://doi.org/10.3934/nhm.2015.10.749
MLA:
Gugat, Martin, et al. "ANALYSIS OF A SYSTEM OF NONLOCAL CONSERVATION LAWS FOR MULTI-COMMODITY FLOW ON NETWORKS." Networks and Heterogeneous Media 10.4 (2015): 749-785.
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