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

##### MSC:
 92D25 Population dynamics (general) 35K55 Nonlinear parabolic equations
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##### References:
 [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 [3] Fisher, R. A.: The advance of advantageous genes. Ann. of eugenics 7, 355-369 (1937) · Zbl 63.1111.04 [4] Friedman, A.: Partial differential equations of parabolic type. (1964) · Zbl 0144.34903 [5] Fujita, H.: On the blowing up of solutions of the Cauchy problem for $ut = {\delta}u + u1 + {\alpha}$. J. fac. Sci. univ. Tokyo, (I) 13, 109-124 (1966) · Zbl 0163.34002 [6] . Amer. math. Soc. trans. 29, 295-381 (1963) [7] Hayakawa, K.: On nonexistence of global solutions of some semilinear parabolic equations. Proc. Japan acad. 49, 503-505 (1973) · Zbl 0281.35039 [8] . Soviet math. Dokl. 1, 533-536 (1960) [9] . Soviet math. Dokl. 2, 48-51 (1961) [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