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On the dynamic programming approach for optimal control problems of PDE’s with age structure. (English) Zbl 1059.49005

Summary: A survey and some new results are presented concerning the dynamic programming for a class of optimal control problems of partial differential equations with age-structure and of delay systems that include some applied examples from economic theory and from population dynamics. A general optimal control problem in Hilbert spaces applying to all examples is investigated, with particular stress on one family of applications: optimal investment models with vintage capital. Some new results are given for the case of constrained investments, including a study of the properties of the optimal trajectories.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
91B28 Finance etc. (MSC2000)
49L20 Dynamic programming in optimal control and differential games
92D25 Population dynamics (general)
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