Existence of solutions in a population dynamics problem
Author:
Gastón E. Hernández
Journal:
Quart. Appl. Math. 43 (1986), 509-521
MSC:
Primary 92A15; Secondary 35K57
DOI:
https://doi.org/10.1090/qam/846161
MathSciNet review:
846161
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Abstract: In this paper we show the existence of a solution for the Gurtin—MacCamy model in population dynamics with age dependence and diffusion. We also discuss the behavior of this solution.
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M. E. Gurtin, A system of equations for age dependent population diffusion, J. Theor. Biol. 40, 389–392 (1973)
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M. E. Gurtin, Some questions and open problems in continuum mechanics and population dynamics, J. Diff. Eq. 48, 293–312 (1983)
M. E. Gurtin, A system of equations for age dependent population diffusion, J. Theor. Biol. 40, 389–392 (1973)
M. E. Gurtin and R. C. MacCamy, Nonlinear age dependent population dynamics, Arch. Rat. Mech. Anal. 54, 281–300 (1974)
M. E. Gurtin and R. C. MacCamy, On the diffusion of biological populations, Math. Bioscience 33, 35–49 (1977)
M. E. Gurtin and R. C. MacCamy, Population dynamics with age dependence, Nonlinear Analysis and Mech. Heriot-Watt Symposium, Vol. III, Pitman, 1979
M. E. Gurtin and R. C. MacCamy, Some simple models for nonlinear age-dependent population dynamics, Math. Biosciences 43, 199–211 (1979)
M. E. Gurtin and R. C. MacCamy, Diffusion models for age-structured population, Math. Biosciences 54, 49–59 (1981)
R. C. MacCamy. A population model with nonlinear diffusion, J. Diff. Equations 39, 52–72 (1981)
G. E. Hernandez, Existence of solutions of population dynamics problems with diffusion, Thesis, University of Minnesota, 1983
A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, 1964
O. A. Ladyženskaja. V. A. Solonikov and N. N. Ural’ceva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., 1968
D. G. Aronson, Regularity properties of flows through porous media: a counterexample, SIAM J. Appl. Math. 19(1970)
D. G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations. Arch. Rat. Mech. Anal. 25, 81–122 (1967)
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Article copyright:
© Copyright 1986
American Mathematical Society