Some Regional Control Problems for Population Dynamics

Laura-Iulia Aniţa (), Sebastian Aniţa (), Vincenzo Capasso () and Ana-Maria Moşneagu ()
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Laura-Iulia Aniţa: “Alexandru Ioan Cuza” University of Iaşi
Sebastian Aniţa: “Alexandru Ioan Cuza” University of Iaşi
Vincenzo Capasso: Universitá degli Studi di Milano
Ana-Maria Moşneagu: “Alexandru Ioan Cuza” University of Iaşi

A chapter in Control Systems and Mathematical Methods in Economics, 2018, pp 419-439 from Springer

Abstract: Abstract This paper deals with some control problems related to structured population dynamics with diffusion. Firstly, we investigate the regional control for an optimal harvesting problem (the control acts in a subregion ω of the whole domain Ω). Using the necessary optimality conditions, for a fixed ω, we get the structure of the harvesting effort which gives the maximum harvest; with this optimal effort we investigate the best choice of the subregion ω in order to maximize the harvest. We introduce an iterative numerical method to increase the total harvest at each iteration by changing the subregion where the effort acts. Numerical tests are used to illustrate the effectiveness of the theoretical results. We also consider the problem of eradication of an age-structured pest population dynamics with diffusion and logistic term, which is a zero-stabilization problem with constraints. We derive a necessary condition and a sufficient condition for zero-stabilizability. We formulate a related optimal control problem which takes into account the cost of intervention in the subregion ω.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-319-75169-6_20

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DOI: 10.1007/978-3-319-75169-6_20

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