An age-dependent population model with nonlinear diffusion in

Author:
Chao Cheng Huang

Journal:
Quart. Appl. Math. **52** (1994), 377-398

MSC:
Primary 92D25; Secondary 35Q80

DOI:
https://doi.org/10.1090/qam/1276244

MathSciNet review:
MR1276244

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References | Similar Articles | Additional Information

**[1]**D. G. Aronson,*Regularity properties of flows through porous media: a counterexample*, SIAM J. Appl. Math.**19**, 299-307 (1970)**[2]**L. A. Caffarelli and A. Friedman,*Continuity of the density of a gas flow in a porous medium*, Trans. Amer. Math. Soc.**252**, 99-113 (1979)**[3]**L. A. Caffarelli and A. Friedman,*Regularity of the free boundary of a gas flow in an n-dimensional porous medium*, Indian Univ. Math. J.**29**, 361-391 (1980)**[4]**E. Dibenedetto and A. Friedman,*Regularity of solutions of nonlinear degenerate parabolic systems*, J. Reine Angew. Math.**349**, 83-128 (1984)**[5]**E. Dibenedetto and A. Friedman,*Holder estimates for nonlinear degenerate parabolic systems*, J. Reine Angew. Math.**357**, 1-22 (1985)**[6]**A. Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, Englewood Cliffs, NJ, 1964**[7]**M. E. Gurtin,*Some questions and open problems in continuum mechanics and population dynamics*, J. Differential Equations**48**, 293-312 (1983)**[8]**M. E. Gurtin and R. C. MacCamy,*Nonlinear age-dependent population dynamics*, Arch. Rational Mech. Anal.**54**, 281-300 (1974)**[9]**M. E. Gurtin and R. C. MacCamy,*Nonlinear dependence population dynamics*, Math. Biosci.**43**, 199-211 (1979)**[10]**M. E. Gurtin and R. C. MacCamy,*Diffusion models for age-structured population*, Math. Biosci.**54**, 49-59 (1981)**[11]**G. E. Hernandez,*Existence of solutions in population dynamic problems*, Quart. Appl. Math.**43**, 509-521 (1986)**[12]**G. E. Hernandez,*Dynamics of population with age dependence and diffusion: localization*, Appl. Anal.**29**, 143-163 (1988)**[13]**G. E. Hernandez,*Anticrowding population models in several space variables*, Quart. Appl. Math.**49**, 87-105 (1991)**[14]**O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural'ceva,*Linear and quasilinear equations of parabolic types*, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968**[15]**R. C. MacCamy,*A population model with nonlinear diffusion*, J. Differential Equations**39**, 52-72 (1981)**[16]**O. A. Oleinik and S. N. Kruzhkov,*Quasilinear second order parabolic equations with many independent variables*, Russian Math. Surveys**16**, 106-146 (1961)**[17]**R. E. Prattle,*Diffusion from an instantaneous point source with concentration-dependent coefficient*, Quart. J. Mech. Appl. Math.**12**, 407-409 (1959)

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Additional Information

DOI:
https://doi.org/10.1090/qam/1276244

Article copyright:
© Copyright 1994
American Mathematical Society