Asymptotic periodicity of flows in time-depending networks

Fatih Bayazit; Britta Dorn; Marjeta Kramar Fijavž; Fatih Bayazit; Britta Dorn; Marjeta Kramar Fijavž

doi:10.3934/nhm.2013.8.843

Networks and Heterogeneous Media

2013, Volume 8, Issue 4: 843-855. doi: 10.3934/nhm.2013.8.843

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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
3.
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana

Received: 01 February 2013 Revised: 01 July 2013
Primary: 35R02; Secondary: 47N20, 37B55.

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.
- Time-depending networks,
- transport equation,
- non-autonomous Cauchy problem,
- evolution family,
- asymptotic periodicity,
- air traffic flow management
Citation: Fatih Bayazit, Britta Dorn, Marjeta Kramar Fijavž. Asymptotic periodicity of flows in time-depending networks[J]. Networks and Heterogeneous Media, 2013, 8(4): 843-855. doi: 10.3934/nhm.2013.8.843

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Abstract

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.

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