Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

On the modeling of moving populations through set evolution equations

Pages: 73 - 98, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.73

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Rinaldo M. Colombo - INdAM Unit, University of Brescia, Via Branze 38, 25123 Brescia, Italy (email)
Thomas Lorenz - RheinMain University of Applied Sciences, Kurt-Schumacher-Ring 18, 65197 Wiesbaden, Germany (email)
Nikolay I. Pogodaev - Institute for System Dynamics and Control Theory, 134 Lermontova st., 664033 Irkutsk, Russian Federation (email)

Abstract: We introduce a class of set evolution equations that can be used to describe population's movements as well as various instances of individual-population interactions. Optimal control/management problems can be formalized and tackled in this framework. A rigorous analytical structure is established and the basic well posedness results are obtained. Several examples show possible applications and their numerical integrations display possible qualitative behaviors of solutions.

Keywords:  Set evolution equations, differential inclusions, evolution of measures, confinement problems, agents-population interactions.
Mathematics Subject Classification:  34A60, 93B03, 34G25.

Received: December 2013;      Revised: March 2014;      Available Online: August 2014.