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Some variational inequalities for age-dependent population dynamics

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Abstract

A variational inequality for an equation of age-dependent population diffusion is studied. A mixed-type boundary condition is prescribed on time-and age-dependent parts of the boundary. The rate of mortality is allowed to have a divergency property at the maximal age.

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References

  1. H. Attouch, Mesurabilité et monotonie. Publications Mathématiques d’Orsay, Orsay, 1976.

    Google Scholar 

  2. H. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam-London-New York, 1973.

    MATH  Google Scholar 

  3. H. Brézis, Problèmes unilatéraux. J. Math. Pures Appl.,51 (1972), 1–168.

    MathSciNet  Google Scholar 

  4. S. Busenberg and M. Iannelli, A class of nonlinear diffusion problems in age-dependent population dynamics. Nonlinear Anal.,7 (1983), 501–529.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Di Blasio, Nonlinear age-dependent population diffusion. J. Math. Biol.,8 (1979), 265–284.

    MATH  MathSciNet  Google Scholar 

  6. M.G. Garroni and L. Lamberti, A variational problem for population dynamics with unilateral constraint. Boll. Un. Mat. Ital., (5)16-B (1979), 876–896.

    MATH  MathSciNet  Google Scholar 

  7. M.G. Garroni and M. Langlais, Age-dependent population diffusion with external constraint. J. Math. Biol.,14 (1982), 77–94.

    Article  MATH  MathSciNet  Google Scholar 

  8. M.E. Gurtin, A system of equations for age-dependent population diffusion. J. Theoret. Biol.,40 (1973), 389–392.

    Article  Google Scholar 

  9. M.E. Gurtin, Some questions and open problems in continuous mechanics and population dynamics. J. Differential Equations,48 (1983), 293–312.

    Article  MATH  MathSciNet  Google Scholar 

  10. N. Kenmochi, Solvability of nonlinear equations with time-dependent constraints and applications. Bull. Fac. Ed., Chiba Univ.,30 (1981), 1–87.

    Google Scholar 

  11. N. Kenmochi, Y. Mizuta and T. Nagai, Projections onto convex sets, convex functions and their subdifferentials. Bull. Fac. Ed., Chiba Univ.,29 (1980), 11–22.

    Google Scholar 

  12. N. Kenmochi and I. Pawlow, Parabolic-elliptic free boundary problems with time-dependent obstacles. Japan J. Appl. Math.,5 (1988), 87–121.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Kubo, Subdifferential operator approach to nonlinear age-dependent population dynamics. Japan J. Appl. Math.,5 (1988), 225–256.

    Article  MATH  MathSciNet  Google Scholar 

  14. R.C. MacCamy, A population model with nonlinear diffusion. J. Differential Equations,39 (1981), 52–72.

    Article  MATH  MathSciNet  Google Scholar 

  15. P. Marcati, Asymptotic behavior in age-dependent population dynamics with hereditary renewal law. SIAM J. Math. Anal.,12 (1981), 904–916.

    Article  MATH  MathSciNet  Google Scholar 

  16. P. Marcati and R. Serafini, Asymptotic behavior in age dependent population dynamics with spatial spread. Boll. Un. Mat. Ital., (5)16-B (1979), 734–753.

    MATH  MathSciNet  Google Scholar 

  17. M. Langlais, On a linear age-dependent population diffusion model. Quart. Appl. Math.,40 (1983), 447–460.

    MATH  MathSciNet  Google Scholar 

  18. M. Langlais, A nonlinear problem in age-dependent population diffusion. SIAM J. Math. Anal.,16 (1985), 510–529.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Langlais, Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion. J. Math. Biol.,26 (1988), 319–346.

    Article  MATH  MathSciNet  Google Scholar 

  20. H.H. Shaefer, Banach Lattices and Positive Operators. Springer-Verlag, Berlin-Heidelberg-New York, 1974.

    Google Scholar 

  21. S. Tucker and S. Zimmerman, A nonlinear model of population dynamics containing an arbitrary number of continuous structure variables. SIAM J. Appl. Math.,48 (1988), 549–591.

    Article  MATH  MathSciNet  Google Scholar 

  22. G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, Inc., New York and Basel, 1985.

    MATH  Google Scholar 

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Kubo, M. Some variational inequalities for age-dependent population dynamics. Japan J. Indust. Appl. Math. 8, 275 (1991). https://doi.org/10.1007/BF03167683

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  • DOI: https://doi.org/10.1007/BF03167683

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