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Networks and Heterogeneous Media

2008, Volume 3, Issue 4: 709-722. doi: 10.3934/nhm.2008.3.709
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Vertex control of flows in networks

  • 1.
    University of L'Aquila, Faculty of Engineering, Piazzale E. Pontieri 2, I-67100 Monteluco di Roio (L’Aquila)
  • 2.
    University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana
  • 3.
    University of Tübingen, Mathematics Institute, Auf der Morgenstelle 10, D-72076 Tübingen
  • 4.
    Eötvös Loránd University Budapest, Department of Applied Analysis, Pázmány Péter sétány 1/c., Budapest H-1117
  • Received: 01 April 2008 Revised: 01 June 2008

  • 34B45, 93B05, 47N70

  • We study a transport equation in a network and control it in a single vertex. We describe all possible reachable states and prove a criterion of Kalman type for those vertices in which the problem is maximally controllable. The results are then applied to concrete networks to show the complexity of the problem.

    Citation: Klaus-Jochen Engel, Marjeta Kramar Fijavž, Rainer Nagel, Eszter Sikolya. Vertex control of flows in networks[J]. Networks and Heterogeneous Media, 2008, 3(4): 709-722. doi: 10.3934/nhm.2008.3.709

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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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