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Nonlinear diffusion in population genetics. (English) Zbl 0361.92020


MSC:

92D25 Population dynamics (general)
92D10 Genetics and epigenetics
34B15 Nonlinear boundary value problems for ordinary differential equations
35K55 Nonlinear parabolic equations
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References:

[1] Aronson, D.G. & H.F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. Lecture Notes in Mathematics 446, 5–49, Springer, New York, 1975. · Zbl 0325.35050
[2] Conley, C., An application of Wazewski’s method to a nonlinear boundary value problem which arises in population genetics, Univ. of Wisconsin Math. Research Center Tech. Summary Report No. 1444, 1975. · Zbl 0314.92004
[3] Fife, P.C. & J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions. To appear. · Zbl 0361.35035
[4] Fisher, R.A., The advance of advantageous genes, Ann. of Eugenics 7, 355–369 (1937). · JFM 63.1111.04
[5] Fleming, W.H., A selection-migration model in population genetics, J. Math. Biology 2, 219–133 (1975). · Zbl 0325.92009
[6] Kolmogoroff, A., I. Petrovsky & N. Piscounoff, Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un probleme biologique, Bull. Univ. Moskou, Ser. Internat., Sec. A, 1 (1937) 6, 1–25. · Zbl 0018.32106
[7] Nagylaki, T., Conditions for the existence of clines, Genetics 80, 595–615 (1975).
[8] Nagylaki, T., Clines with variable migration, to appear in Genetics. · Zbl 1322.92037
[9] Oleinik, O.A. & S.N. Kružkov, Quasilinear second order parabolic equations with many independent variables. Russian Math. Surveys, 16, 105–146 (1961). · Zbl 0112.32604
[10] Sattinger, D. H., Topics in stability and bifurcation theory, Lecture Notes in Mathematics 309, Springer, New York, 1973. · Zbl 0248.35003
[11] Titchmarsh, E.C., Eigenfunction expansions, Part II, Chapter XVI, Oxford University Press London, 1958. · Zbl 0097.27601
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