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Optimal strategies for a time-dependent harvesting problem. (English) Zbl 1405.35099

Summary: 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.

MSC:

35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
35Q93 PDEs in connection with control and optimization
49J20 Existence theories for optimal control problems involving partial differential equations
49N25 Impulsive optimal control problems
49N90 Applications of optimal control and differential games
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References:

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