Optimal strategies for a time-dependent harvesting problem

2016/02/18 by G. M. Coclite, Coclite, G. M., M. Garavello +3
Mathematics · #35K61 #35Q93 #49J20 #49N25 #49N90 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K61 #msc:35Q93 #msc:49J20 #msc:49N25 #msc:49N90

paper · pdf · doi:10.48550/arxiv.1602.05737

44 pages

arxiv created 2016/02/18 · arxiv updated 2016/02/19

Abstract

We focus on an optimal control problem, introduced by Bressan and Shen 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.

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