Aronson, D. G.; Weinberger, H. F. Multidimensional nonlinear diffusion arising in population genetics. (English) Zbl 0407.92014 Adv. Math. 30, 33-76 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 833 Documents MSC: 92D25 Population dynamics (general) 35K55 Nonlinear parabolic equations Keywords:Population Genetics; Multidimensional Nonlinear Diffusion; Parabolic Equations; Plane Wave Solutions; Large Time Behaviour of Solutions; Perturbation; Initial Value Problems Citations:Zbl 0325.35050 PDF BibTeX XML Cite \textit{D. G. Aronson} and \textit{H. F. Weinberger}, Adv. Math. 30, 33--76 (1978; Zbl 0407.92014) Full Text: DOI OpenURL References: [1] Aronson, D.G; Weinberger, H.F, Nonlinear diffusion in population genetics, combustion, and nerve propagation, (), 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 Englewood Cliffs, New Jersey · Zbl 0144.34903 [5] Fujita, H, On the blowing up of solutions of the Cauchy problem for ut = δu + u1 + α, J. fac. sci. univ. Tokyo, (I), 13, 109-124, (1966) · Zbl 0163.34002 [6] Gelfand, I.M, Some problems in the theory of quasilinear equations, Uspehi math. nauk, Amer. math. soc. trans., 29, 295-381, (1963) · Zbl 0127.04901 [7] Hayakawa, K, On nonexistence of global solutions of some semilinear parabolic equations, (), 503-505 · Zbl 0281.35039 [8] Kanel’, Ja.I, The behavior of solutions of the Cauchy problem when time tends to infinity, in the case of quasilinear equations arising in the theory of combustion, Dokl. akad. nauk S.S.S.R., Soviet math. dokl., 1, 533-536, (1960) · Zbl 0152.10301 [9] Kanel’, Ja.I, Certain problems on equations in the theory of burning, Dokl. akad. nauk S.S.S.R., 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 [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) [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; Petrovski, I.G, Ordinary differential equations, (1973), Dover New York [15] Protter, M.H; Weinberger, H.F, Maximum principles in differential equations, (1967), Prentice-Hall Englewood Cliffs, New Jersey · Zbl 0153.13602 [16] {\scT. Sirao}, On the growing up problem for semilinear heat equations, Kokyuroku of the Inst. of Math., Anal., Kyoto Univ., in press. · 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.