On the modeling of moving populations through set evolution equations

Rinaldo M. Colombo; Thomas Lorenz; Nikolay I. Pogodaev

doi:10.3934/dcds.2015.35.73

Article Contents

2015, Volume 35, Issue 1: 73-98. Doi: 10.3934/dcds.2015.35.73

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On the modeling of moving populations through set evolution equations

1.
INdAM Unit, University of Brescia, Via Branze 38, 25123 Brescia
2.
RheinMain University of Applied Sciences, Kurt-Schumacher-Ring 18, 65197 Wiesbaden
3.
Institute for System Dynamics and Control Theory, 134 Lermontova st., 664033 Irkutsk

Received: November 30, 2013

Revised: February 28, 2014

Published: December 2014

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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.

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Mathematics Subject Classification: 34A60, 93B03, 34G25.

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