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
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