Control of biological resources on graphs
1 INDAM Unit, University of Brescia, Via Branze 38, 25123 Brescia, Italy.
2 Department of Mathematics and Applications, University of Milano, Bicocca, Via R. Cozzi 55, 20125 Milano, Italy.
Received: 18 August 2015
Revised: 4 May 2016
Accepted: 17 May 2016
A biological resource is a population characterized by birth, aging and death, grown in order to produce a profit. The evolution of this system is described by a structured population model, modified to take into account the selection for reproduction or for the market. This selection is the control that has to be optimized in order to maximize the profit. First we prove the well posedness of the descriptive model. Then, the profit is shown to be Gâteaux differentiable with respect to the controls. Finally, we ensure that the maximal profit can be reached by means of Bang–Bang controls.
Mathematics Subject Classification: 35L50 / 35Q92 / 35Q93
Key words: Conservation Laws / optimal control problems / management of biological resources / structured population dynamics
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