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

92D25Population dynamics (general)
35K55Nonlinear parabolic equations
Full Text: DOI
[1] Aronson, D. G.; Weinberger, H. F.: Nonlinear diffusion in population genetics, combustion, and nerve propagation. Partial differential equations and related topics, lecture notes in mathematics 446, 5-49 (1975)
[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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[10] Kanel’, Ja.I: Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory. Mat. sbornik 59, No. 101, 245-288 (1962) · 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, No. 107, 398-413 (1964)
[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)
[15] Protter, M. H.; Weinberger, H. F.: Maximum principles in differential equations. (1967) · Zbl 0153.13602
[16] T. Sirao, On the growing up problem for semilinear heat equations, Kokyuroku of the Inst. of Math., Anal., Kyoto Univ., in press. · Zbl 0353.35057