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Pontryagin's principle for control problems in age-dependent population dynamics

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Abstract

In this paper, Pontryagin's principle is proved for a fairly general problem of optimal control of populations with continuous time and age variable. As a consequence, maximum principles are developed for an optimal harvesting problem and a problem of optimal birth control.

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References

  1. Castaing, C., Valadier, M.: Convex analysis and measurable multifunctions. Lect. Notes Math. 580, Berlin-Heidelberg-New York: Springer 1977

  2. Clark, C. W.: Mathematical bioeconomics: the optimal management of renewable resources. New York: Wiley 1976

    Google Scholar 

  3. Getz, W.: Optimal harvesting of structured populations. Math. Biosci. 44, 269–291 (1979)

    Google Scholar 

  4. Girsanov, I.: Lectures on mathematical theory of extremum problems. Lect. Notes Econ. Math. Systems 67. Berlin-Heidelberg-New York: Springer 1972

  5. Gurtin, M., MacCamy, R: Non-linear age-dependent population dynamics. Arch. Ration. Mech. Anal. 54, 281–300 (1974)

    Google Scholar 

  6. Gurtin, M., Murphy, L.: On the optimal harvesting of age-structured populations. In: Busenberg, S., Cooke, K. (eds.) Differential equations and applications in ecology, epidemics, and population problems, pp. 115–129. New York: Academic Press 1981

    Google Scholar 

  7. Gurtin, M., Murphy, L.: On the optimal harvesting of age-structured populations: some simple models. Math. Biosci. 55, 115–136 (1981)

    Google Scholar 

  8. Gurtin, M., Murphy, L.: On the optimal harvesting of persistent age-structured populations. J. Math. Biol. 13, 131–148 (1981)

    Google Scholar 

  9. Ioffe, A., Tihomirov, V.: Theory of extremal problems. Amsterdam: North-Holland 1979 (Russian edn.: Nauka, Moscow 1974)

    Google Scholar 

  10. Marcus, M., Mizel, V.: Semilinear hereditary hyperbolic systems with nonlocal boundary conditions. J. Math. Anal. Appl. 76, 440–475 (1980) and 77, 1–19 (1980)

    Google Scholar 

  11. Murphy, L.: A nonlinear growth mechanism in size structured population dynamics. J. Theor. Biol. 104, 493–506 (1983)

    Google Scholar 

  12. Neustadt, L.: Optimization: a theory of necessary condition. Princeton: Princeton University Press 1976

    Google Scholar 

  13. Zowe, J., Kurcyusz, S.: Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5, 49–62 (1979)

    Google Scholar 

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  1. Institut f. Mathematik, Universität Augsburg, D-8900, Augsburg, Federal Republic of Germany

    Martin Brokate

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  1. Martin Brokate
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Brokate, M. Pontryagin's principle for control problems in age-dependent population dynamics. J. Math. Biology 23, 75–101 (1985). https://doi.org/10.1007/BF00276559

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  • DOI: https://doi.org/10.1007/BF00276559

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