In this lecture we consider a model for the harvesting of marine resources. Since the cost functionals have linear growth with respect to the pointwise intensity of fishing effort, optimal solutions are in general measure-valued. For the control problem, we prove the existence of optimal strategies.
Those results were obtained in collaboration with A. Bressan, G. Devillanova, M. Garavello, W. Shen, S. F. Solimini, L. V. Spinolo.