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Multidimensional nonlinear diffusion arising in population genetics. (English) Zbl 0407.92014


MSC:

92D25 Population dynamics (general)
35K55 Nonlinear parabolic equations

Citations:

Zbl 0325.35050
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Full Text: DOI

References:

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[2] Chafee, N., A stability analysis for a semilinear parabolic partial differential equation, J. Differential Eqs., 15, 522-540 (1974) · Zbl 0271.35043
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[4] Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey · Zbl 0144.34903
[5] Fujita, H., On the blowing up of solutions of the Cauchy problem for \(u_t = Δu + u^{1 + α} \), J. Fac. Sci. Univ. Tokyo, (I), 13, 109-124 (1966) · Zbl 0163.34002
[6] Amer. Math. Soc. Trans., 29, 295-381 (1963) · Zbl 0127.04901
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[9] Soviet Math. Dokl., 2, 48-51 (1961) · Zbl 0138.35103
[10] Kanel’, Ja. I., Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory, Mat. Sbornik, 59, 101, 245-288 (1962), supplement · Zbl 0152.10302
[11] Kanel’, Ja. I., On the stability of solutions of the equations of combustion theory for finite initial functions, Mat. Sbornik, 65, 107, 398-413 (1964) · Zbl 0168.36301
[12] Kobayashi, K.; Sirao, T.; Tanaka, H., On the growing up problem for semilinear heat equations, J. Math. Soc. Japan, 29, 407-424 (1977) · Zbl 0353.35057
[13] Kolmogoroff, A.; Petrovsky, I.; Piscounoff, N., Étude de l’équations de la diffusion avec croissance de la quantité de matière et son application a un problème biologique, Bull. Univ. Moscow, Ser. Internat., Sec. A, 1, 1-25 (1937) · Zbl 0018.32106
[14] Petrovski, I. G., Ordinary Differential Equations (1973), Dover: Dover New York · Zbl 0279.34001
[15] Protter, M. H.; Weinberger, H. F., Maximum Principles in Differential Equations (1967), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey · Zbl 0153.13602
[16] T. Sirao; T. Sirao · Zbl 0353.35057
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