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Optimal harvesting for periodic age-dependent population dynamics. (English) Zbl 0935.92030

The authors investigate optimal periodic control of the Lotka-McKendrick equations for age-dependent population dynamics subject to periodic vital rates and periodic forcing. They prove existence and uniqueness of a periodic solution to the equations for given controls as well as existence of an optimal control and a bang-bang principle. In some cases, also uniqueness follows. They also prove linear convergence of an implicit first order discretization of the adjoint system and use this to numerically compute the optimal control in some examples.

MSC:

92D25 Population dynamics (general)
49N90 Applications of optimal control and differential games
65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
45D05 Volterra integral equations
35B10 Periodic solutions to PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
92D40 Ecology
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