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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

Cite

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, Vol. 446 (1975), Springer: Springer New York), 5-49 ·Zbl 0325.35050
[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) ·JFM 63.1111.04
[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
[7]Hayakawa, K., On nonexistence of global solutions of some semilinear parabolic equations, (Proc. Japan Acad., 49 (1973)), 503-505 ·Zbl 0281.35039
[8]Soviet Math. Dokl., 1, 533-536 (1960) ·Zbl 0152.10301
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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