Optimal strategies for a time-dependent harvesting problem

Giuseppe Maria Coclite; Mauro Garavello; Laura V. Spinolo

doi:10.3934/dcdss.2018053

Article Contents

2018, Volume 11, Issue 5: 865-900. Doi: 10.3934/dcdss.2018053

This issue Previous Article Measure-theoretic Lie brackets for nonsmooth vector fields Next Article One-dimensional, forward-forward mean-field games with congestion

Optimal strategies for a time-dependent harvesting problem

1.
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy
2.
Department of Mathematics and its Applications, University of Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy
3.
IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy

Received: January 31, 2017

Revised: February 28, 2017

Published: June 2018

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Abstract

We focus on an optimal control problem, introduced by Bressan and Shen in [5] as a model for fish harvesting. We consider the time-dependent case and we establish existence and uniqueness of an optimal strategy. We also study a related differential game, 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 focuses on one-dimensional fishing domains.

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Mathematics Subject Classification: Primary: 35K61, 35Q93, 49J20; Secondary: 49N25, 49N90.

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References

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