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

Coclite, G., Garavello, M., Spinolo, L. (2018). Optimal strategies for a time-dependent harvesting problem. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 11(5), 865-900 [10.3934/dcdss.2018053].

Optimal strategies for a time-dependent harvesting problem

Garavello, Mauro;
2018

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
Articolo in rivista - Articolo scientifico
Differential games; Fish harvesting; Measured-valued solutions; Optimal control; Analysis; Discrete Mathematics and Combinatorics; Applied Mathematics
English
2018
11
5
865
900
none
Coclite, G., Garavello, M., Spinolo, L. (2018). Optimal strategies for a time-dependent harvesting problem. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 11(5), 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/10281/213683
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