Control of biological resources on graphs

Author: Colombo Rinaldo M.   Garavello Mauro  

Publisher: Edp Sciences

E-ISSN: 1262-3377|23|3|1073-1097

ISSN: 1292-8119

Source: ESAIM: Control, Optimisation and Calculus of Variations, Vol.23, Iss.3, 2017-05, pp. : 1073-1097

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Abstract

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.