An age-dependent population model with nonlinear diffusion in $\textbf {R}^n$
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
Full-text PDF Free Access
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Additional Information
D. G. Aronson, Regularity properties of flows through porous media: a counterexample, SIAM J. Appl. Math. 19, 299β307 (1970)
L. A. Caffarelli and A. Friedman, Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252, 99β113 (1979)
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, 361β391 (1980)
E. Dibenedetto and A. Friedman, Regularity of solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math. 349, 83β128 (1984)
E. Dibenedetto and A. Friedman, Holder estimates for nonlinear degenerate parabolic systems, J. Reine Angew. Math. 357, 1β22 (1985)
A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, NJ, 1964
M. E. Gurtin, Some questions and open problems in continuum mechanics and population dynamics, J. Differential Equations 48, 293β312 (1983)
M. E. Gurtin and R. C. MacCamy, Nonlinear age-dependent population dynamics, Arch. Rational Mech. Anal. 54, 281β300 (1974)
M. E. Gurtin and R. C. MacCamy, Nonlinear dependence population dynamics, Math. Biosci. 43, 199β211 (1979)
M. E. Gurtin and R. C. MacCamy, Diffusion models for age-structured population, Math. Biosci. 54, 49β59 (1981)
G. E. Hernandez, Existence of solutions in population dynamic problems, Quart. Appl. Math. 43, 509β521 (1986)
G. E. Hernandez, Dynamics of population with age dependence and diffusion: localization, Appl. Anal. 29, 143β163 (1988)
G. E. Hernandez, Anticrowding population models in several space variables, Quart. Appl. Math. 49, 87β105 (1991)
O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Uralβceva, Linear and quasilinear equations of parabolic types, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968
R. C. MacCamy, A population model with nonlinear diffusion, J. Differential Equations 39, 52β72 (1981)
O. A. Oleinik and S. N. Kruzhkov, Quasilinear second order parabolic equations with many independent variables, Russian Math. Surveys 16, 106β146 (1961)
R. E. Prattle, Diffusion from an instantaneous point source with concentration-dependent coefficient, Quart. J. Mech. Appl. Math. 12, 407β409 (1959)
D. G. Aronson, Regularity properties of flows through porous media: a counterexample, SIAM J. Appl. Math. 19, 299β307 (1970)
L. A. Caffarelli and A. Friedman, Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252, 99β113 (1979)
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, 361β391 (1980)
E. Dibenedetto and A. Friedman, Regularity of solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math. 349, 83β128 (1984)
E. Dibenedetto and A. Friedman, Holder estimates for nonlinear degenerate parabolic systems, J. Reine Angew. Math. 357, 1β22 (1985)
A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, NJ, 1964
M. E. Gurtin, Some questions and open problems in continuum mechanics and population dynamics, J. Differential Equations 48, 293β312 (1983)
M. E. Gurtin and R. C. MacCamy, Nonlinear age-dependent population dynamics, Arch. Rational Mech. Anal. 54, 281β300 (1974)
M. E. Gurtin and R. C. MacCamy, Nonlinear dependence population dynamics, Math. Biosci. 43, 199β211 (1979)
M. E. Gurtin and R. C. MacCamy, Diffusion models for age-structured population, Math. Biosci. 54, 49β59 (1981)
G. E. Hernandez, Existence of solutions in population dynamic problems, Quart. Appl. Math. 43, 509β521 (1986)
G. E. Hernandez, Dynamics of population with age dependence and diffusion: localization, Appl. Anal. 29, 143β163 (1988)
G. E. Hernandez, Anticrowding population models in several space variables, Quart. Appl. Math. 49, 87β105 (1991)
O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Uralβceva, Linear and quasilinear equations of parabolic types, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968
R. C. MacCamy, A population model with nonlinear diffusion, J. Differential Equations 39, 52β72 (1981)
O. A. Oleinik and S. N. Kruzhkov, Quasilinear second order parabolic equations with many independent variables, Russian Math. Surveys 16, 106β146 (1961)
R. E. Prattle, Diffusion from an instantaneous point source with concentration-dependent coefficient, Quart. J. Mech. Appl. Math. 12, 407β409 (1959)
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Article copyright:
© Copyright 1994
American Mathematical Society
