Control of biological resources on graphs
Rinaldo M. Colombo and Mauro Garavello
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.