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Existence and uniqueness of solutions for a nonlinear diffusion problem arising in population genetics

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References

  1. H. Amann, “On the existence of positive solutions of nonlinear elliptic boundary value problems”, Indiana Univ. Math. J. 21, 2, 125–146 (1971).

    Google Scholar 

  2. D. G. Aronson & H. F. Weinberger, Nonlinear Diffusion in Population Genetics, Combustion and Nerve Pulse Propagation, in “Partial Equations and Related Topics”, Lecture Notes in Mathematics, Vol. 446, 5–49, Springer, New York, 1975.

    Google Scholar 

  3. D. G. Aronson & H. F. Weinberger, “Multidimensional nonlinear diffusion arising in population genetics”, Adv. in Math. 30, 33–76 (1978).

    Google Scholar 

  4. J. M. Ball, “Differentiability properties of symmetric and isotropic functions,” Duke Math. J. 51, 3, 699–728 (1984).

    Google Scholar 

  5. Coddington, & Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955.

  6. C. Conley, “An application of Wazewski's method to a non-linear boundary value problem which arises in population genetics”. J. Math. Biol. 2, 241–249 (1975).

    Google Scholar 

  7. P. C. Fife & L. A. Peletier, “Nonlinear diffusion in population genetics”, Arch. Rational Mech. Anal. 64, 93–109 (1977).

    Google Scholar 

  8. W. H. Fleming, “A selection-migration model in population genetics”, J. Math. Biol. 2, 219–233 (1975).

    Google Scholar 

  9. B. Gidas, W. M. Ni & L. Nirenberg, “Symmetry and related properties via the maximum principle”, Comm. Math. Phys. 68, 209–243 (1979).

    Google Scholar 

  10. H. B. Keller & D. S. Cohen, “Some position problems suggested by nonlinear heat generation”, J. Math. Mech. 16, 12, 1361–1376 (1967).

    Google Scholar 

  11. T. Nagylaki, “Conditions for the existence of clines”, Genetics 80, 595–615 July, (1975).

    Google Scholar 

  12. W. M. Ni, “On the elliptic equation 317-01, its generalizations and applications in geometry”, Indiana Univ. Math. J. 31, 4, 493–529 (1982).

    Google Scholar 

  13. L. A. Peletier & J. Serrin, “Uniqueness of positive solutions of semilinear equations in ℝn,” Arch. Rational Mech. Anal. 81, 181–197 (1983).

    Google Scholar 

  14. L. A. Peletier & J. Serrin, “Uniqueness of non-negative solutions of semilinear equations in ℝn”, J. Differential Equations 61, 380–397 (1986).

    Google Scholar 

  15. M. Slatkin, “Gene flow and selection in a cline”, Genetics 75, 733–756 Dec., (1973).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Edinburgh

    Achilles Tertikas

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  1. Achilles Tertikas
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Communicated by J. Serrin

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Tertikas, A. Existence and uniqueness of solutions for a nonlinear diffusion problem arising in population genetics. Arch. Rational Mech. Anal. 103, 289–317 (1988). https://doi.org/10.1007/BF00251443

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