Calculus of Variations and Geometric Measure Theory

G. M. Coclite - M. Garavello - L. V. Spinolo

Optimal strategies for a time-dependent harvesting problem

created by coclite on 16 Feb 2016


Submitted Paper

Inserted: 16 feb 2016
Last Updated: 16 feb 2016

Pages: 44
Year: 2016


We focus on an optimal control problem, introduced by Bressan and Shen in~\cite{BS1} as a model for fish harvesting. We consider the time-dependent case and we establish existence and uniqueness of an optimal strategy, and sufficient conditions for optimality. We also consider a related differential game that models the situation where there are several competing fish companies and we prove existence of Nash equilibria. From the technical viewpoint, the most relevant point is establishing the uniqueness result. This amounts to prove precise a-priori estimates for solutions of suitable parabolic equations with measure-valued coefficients. All the analysis is developed in the case when the fishing domain is one-dimensional.

Keywords: optimal control, differential games, measured-valued solutions, fish harvest