Some nonlinear degenerate diffusion equations related to population dynamics

Toshitaka NAGAI; Masayasu MIMURA

doi:10.2969/jmsj/03530539

Toshitaka NAGAI, Masayasu MIMURA

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JOURNAL FREE ACCESS

1983 Volume 35 Issue 3 Pages 539-562

DOI https://doi.org/10.2969/jmsj/03530539

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Published: 1983 Received: September 12, 1981 Available on J-STAGE: October 20, 2006 Accepted: June 26, 1982 Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D.G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math., 17 (1969), 461-467.
2) D.G. Aronson, Regularity properties of flows through porous media: A counterexample, SIAM J. Appl. Math., 19 (1970), 299-307.
3) A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Eagle. wood Cliffs, N.J., 1964.
4) B.H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc., 13 (1976), 103-106.
5) B.H. Gilding, Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal., 65 (1977), 203-225.
6) B.H. Gilding, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa, 4 (1977), 393-432.
7) B.H. Gilding and L. A. Peletier, The Cauchy problem for an equation in the theory of infiltration, Arch. Rational Mech. Anal., 61 (1976), 127-140.
8) W.S.C. Gurney and R.M. Nisbet, The regulation of inhomogeneous populations, J. Theoret. Biol., 52 (1975), 441-457.
9) M.E. Gurtin and R.C. MacCamy, On the diffusion of biological populations, Math. Biosci., 33 (1979), 35-49.
10) W.D. Hamilton, Geometry for the selfish herd, J. Theoret. Biol., 31 (1971), 295-311.
11) O.A. Ladyzenskaja, V.A. Solonikov and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, 23, Amer. Math. Soc., Providence, R.I., 1968.
12) T. Nagai and M. Mimura, Asymptotic behavior for a nonlinear degenerate diffusion equation in population dynamics, SIAM J. Appl. Math., (to appear).
13) O.A. Oleinik, A.S. Kalashnikov and Chzou Yui-Lin, The Cauchy problem and boundary value problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk SSSR, 22 (1958), 667-704, (Russian).

Right : [1] D. G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math., 17 (1969), 461-467.
[2] D. G. Aronson, Regularity properties of flows through porous media: A counterexample, SIAM J. Appl. Math., 19 (1970), 299-307.
[3] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Eagle-wood Cliffs, N. J., 1964.
[4] B. H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc., 13 (1976), 103-106.
[5] B. H. Gilding, Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal., 65 (1977), 203-225.
[6] B. H. Gilding, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa, 4 (1977), 393-432.
[7] B. H. Gilding and L. A. Peletier, The Cauchy problem for an equation in the theory of infiltration, Arch. Rational Mech. Anal., 61 (1976), 127-140.
[8] W. S. C. Gurney and R. M. Nisbet, The regulation of inhomogeneous populations, J. Theoret. Biol., 52 (1975), 441-457.
[9] M. E. Gurtin and R. C. MacCamy, On the diffusion of biological populations, Math. Biosci., 33 (1979), 35-49.
[10] W. D. Hamilton, Geometry for the selfish herd, J. Theoret. Biol., 31 (1971), 295-311.
[11] O. A. Ladyzenskaja, V. A. Solonikov and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Translations of Mathematical Monographs, 23, Amer. Math. Soc., Providence, R. I., 1968.
[12] T. Nagai and M. Mimura, Asymptotic behavior for a nonlinear degenerate diffusion equation in population dynamics, SIAM J. Appl. Math., (to appear).
[13] O. A. Oleinik, A. S. Kalashnikov and Chzou Yui-Lin, The Cauchy problem and boundary value problems for equations of the type of nonstationary filtration, Izv. Akad. Nauk SSSR, 22 (1958), 667-704, (Russian).

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