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 | References | Similar Articles | Additional Information

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.

**[1]**M. E. Gurtin,*Some questions and open problems in continuum mechanics and population dynamics*, J. Diff. Eq.**48**, 293-312 (1983) MR**696872****[2]**M. E. Gurtin,*A system of equations for age dependent population diffusion*, J. Theor. Biol.**40**, 389-392 (1973)**[3]**M. E. Gurtin and R. C. MacCamy,*Nonlinear age dependent population dynamics*, Arch. Rat. Mech. Anal.**54**, 281-300 (1974) MR**0354068****[4]**M. E. Gurtin and R. C. MacCamy,*On the diffusion of biological populations*, Math. Bioscience**33**, 35-49 (1977) MR**0682594****[5]**M. E. Gurtin and R. C. MacCamy,*Population dynamics with age dependence*, Nonlinear Analysis and Mech. Heriot-Watt Symposium, Vol. III, Pitman, 1979 MR**539689****[6]**M. E. Gurtin and R. C. MacCamy,*Some simple models for nonlinear age-dependent population dynamics*, Math. Biosciences**43**, 199-211 (1979) MR**527566****[7]**M. E. Gurtin and R. C. MacCamy,*Diffusion models for age-structured population*, Math. Biosciences**54**, 49-59 (1981) MR**630655****[8]**R. C. MacCamy.*A population model with nonlinear diffusion*, J. Diff. Equations**39**, 52-72 (1981) MR**602431****[9]**G. E. Hernandez,*Existence of solutions of population dynamics problems with diffusion*, Thesis, University of Minnesota, 1983 MR**2633078****[10]**A. Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, 1964 MR**0181836****[11]**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 MR**0241822****[12]**D. G. Aronson,*Regularity properties of flows through porous media: a counterexample*, SIAM J. Appl. Math.**19**(1970) MR**0265774****[13]**D. G. Aronson and J. Serrin,*Local behavior of solutions of quasilinear parabolic equations*. Arch. Rat. Mech. Anal.**25**, 81-122 (1967) MR**0244638**

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Additional Information

DOI:
https://doi.org/10.1090/qam/846161

Article copyright:
© Copyright 1986
American Mathematical Society