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.

Optimal strategies for a time-dependent harvesting problem / Coclite, Giuseppe Maria; Garavello, Mauro; Spinolo, Laura V.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - STAMPA. - 11:5(2018), pp. 865-900. [10.3934/dcdss.2018053]

Optimal strategies for a time-dependent harvesting problem

Giuseppe Maria Coclite
;
2018-01-01

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.
2018
Optimal strategies for a time-dependent harvesting problem / Coclite, Giuseppe Maria; Garavello, Mauro; Spinolo, Laura V.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - STAMPA. - 11:5(2018), pp. 865-900. [10.3934/dcdss.2018053]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93917
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