# American Institute of Mathematical Sciences

December  2013, 8(4): 843-855. doi: 10.3934/nhm.2013.8.843

## Asymptotic periodicity of flows in time-depending networks

 1 Universität Tübingen, Mathematisch-Naturwissenschaftliche Fakultät, Auf der Morgenstelle 10, D-72076 Tübingen 2 WSI für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany 3 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia

Received  February 2013 Revised  July 2013 Published  November 2013

We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the solutions under certain natural conditions on the network. We further apply our theory to a model used for air traffic flow management.
Citation: Fatih Bayazit, Britta Dorn, Marjeta Kramar Fijavž. Asymptotic periodicity of flows in time-depending networks. Networks & Heterogeneous Media, 2013, 8 (4) : 843-855. doi: 10.3934/nhm.2013.8.843
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