×

zbMATH — the first resource for mathematics

Optimal harvesting control problem for linear periodic age-dependent population dynamics. (English) Zbl 1043.92039
Summary: We investigate an optimal harvesting problem for linear periodic age-dependent population dynamics. Namely, we consider the Lotka-McKendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. By Mazur’s Theorem, we demonstrate existence of solutions of the optimal control problem, and by the conception of normal cones, we also obtain first order necessary conditions of optimality for that problem. Finally, under suitable assumptions, we give uniqueness of solutions of the optimal control problem. Our results extend some known criteria.

MSC:
92D40 Ecology
49N90 Applications of optimal control and differential games
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
49J22 Optimal control problems with integral equations (existence) (MSC2000)
49K22 Optimal control problems with integral equations (nec./ suff.) (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ianelli, M., Mathematical theory of age-structured population dynamics, CNR applied mathematics monographs, vol. 7, (1995), Giardini Editori e Stampatori Pisa
[2] Brokate, M., Pontryagin’s principle for control problems in age-dependent population dynamics, J. math. biol., 23, 75-101, (1985) · Zbl 0599.92017
[3] M. Brokate, On a certain optimal harvesting problem with continuous age-structure, in: Optimal Control of Partial Differential Equitions II, Birkhäuser, 1987, pp. 29-42
[4] Gurtin, M.E.; Murphy, L.F., On the optimal harvesting of age-structured populations: some simple models, Math. biosci., 55, 115-136, (1981) · Zbl 0467.92017
[5] Gurtin, M.E.; Murphy, L.F., On the optimal harvesting of persistent age-structured populations, J. math. biol., 13, 131-148, (1981) · Zbl 0466.92021
[6] Murphy, L.F.; Smith, S.J., Optimal harvesting of an age-structured population, J. math. biol., 29, 77-90, (1990) · Zbl 0737.92025
[7] Anita, S., Optimal harvesting for a nonlinear age-dependent population dynamics, J. math. anal. appl., 226, 6-12, (1998) · Zbl 0980.92027
[8] Anita, S., Optimal control of a nonlinear population dynamics with diffusion, J. math. anal. appl., 152, 176-208, (1990) · Zbl 0731.92022
[9] Anita, S., Analysis and control of age-dependent population dynamics, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0960.92026
[10] Anita, S.; Iannelli, M.; Kim, M.Y.; Park, E.J., Optimal harvesting for periodic age-dependent population dynamics, SIAM J. appl. math., 58, 1648-1666, (1998) · Zbl 0935.92030
[11] Barbu, V.; Precupanu, T., Convexity and optimization in Banach spaces, (1986), D. Reidel Publishing Company Dordrecht, Boston · Zbl 0594.49001
[12] Web, G., Theory of nonlinear age-dependent population dynamics, (1985), Dekker New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.