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.
Similar content being viewed by others
References
H. Attouch, Mesurabilité et monotonie. Publications Mathématiques d’Orsay, Orsay, 1976.
H. Brézis, Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam-London-New York, 1973.
H. Brézis, Problèmes unilatéraux. J. Math. Pures Appl.,51 (1972), 1–168.
S. Busenberg and M. Iannelli, A class of nonlinear diffusion problems in age-dependent population dynamics. Nonlinear Anal.,7 (1983), 501–529.
G. Di Blasio, Nonlinear age-dependent population diffusion. J. Math. Biol.,8 (1979), 265–284.
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.
M.G. Garroni and M. Langlais, Age-dependent population diffusion with external constraint. J. Math. Biol.,14 (1982), 77–94.
M.E. Gurtin, A system of equations for age-dependent population diffusion. J. Theoret. Biol.,40 (1973), 389–392.
M.E. Gurtin, Some questions and open problems in continuous mechanics and population dynamics. J. Differential Equations,48 (1983), 293–312.
N. Kenmochi, Solvability of nonlinear equations with time-dependent constraints and applications. Bull. Fac. Ed., Chiba Univ.,30 (1981), 1–87.
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.
N. Kenmochi and I. Pawlow, Parabolic-elliptic free boundary problems with time-dependent obstacles. Japan J. Appl. Math.,5 (1988), 87–121.
M. Kubo, Subdifferential operator approach to nonlinear age-dependent population dynamics. Japan J. Appl. Math.,5 (1988), 225–256.
R.C. MacCamy, A population model with nonlinear diffusion. J. Differential Equations,39 (1981), 52–72.
P. Marcati, Asymptotic behavior in age-dependent population dynamics with hereditary renewal law. SIAM J. Math. Anal.,12 (1981), 904–916.
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.
M. Langlais, On a linear age-dependent population diffusion model. Quart. Appl. Math.,40 (1983), 447–460.
M. Langlais, A nonlinear problem in age-dependent population diffusion. SIAM J. Math. Anal.,16 (1985), 510–529.
M. Langlais, Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion. J. Math. Biol.,26 (1988), 319–346.
H.H. Shaefer, Banach Lattices and Positive Operators. Springer-Verlag, Berlin-Heidelberg-New York, 1974.
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.
G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, Inc., New York and Basel, 1985.
Author information
Authors and Affiliations
About this article
Cite this article
Kubo, M. Some variational inequalities for age-dependent population dynamics. Japan J. Indust. Appl. Math. 8, 275 (1991). https://doi.org/10.1007/BF03167683
Received:
Revised:
DOI: https://doi.org/10.1007/BF03167683