Calculus of Variations and Geometric Measure Theory

G. M. Coclite - M. Garavello

A Time Dependent Optimal Harvesting Problem with Measure Valued Solutions

created by coclite on 16 Feb 2016


Submitted Paper

Inserted: 16 feb 2016
Last Updated: 16 feb 2016

Pages: 18
Year: 2016


The paper is concerned with the optimal harvesting of a marine park, which is described by a parabolic heat equation with Neumann boundary conditions and a nonlinear source term. We consider a cost functional, which is linear with respect to the control; hence the optimal solution can belong to the class of measure-valued control strategies. For each control function, we prove existence, and stability estimates for solutions of the parabolic equation. Moreover, we prove the existence of an optimal solution. Finally, some numerical simulations conclude the paper.

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