Skip to main content
Log in

Nonlinear diffusion in population genetics

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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.

  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.

  3. Fife, P.C. & J.B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions. To appear.

  4. Fisher, R.A., The advance of advantageous genes, Ann. of Eugenics 7, 355–369 (1937).

    Google Scholar 

  5. Fleming, W.H., A selection-migration model in population genetics, J. Math. Biology 2, 219–133 (1975).

    Google Scholar 

  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.

    Google Scholar 

  7. Nagylaki, T., Conditions for the existence of clines, Genetics 80, 595–615 (1975).

    Google Scholar 

  8. Nagylaki, T., Clines with variable migration, to appear in Genetics.

  9. Oleinik, O.A. & S.N. Kružkov, Quasilinear second order parabolic equations with many independent variables. Russian Math. Surveys, 16, 105–146 (1961).

    Google Scholar 

  10. Sattinger, D. H., Topics in stability and bifurcation theory, Lecture Notes in Mathematics 309, Springer, New York, 1973.

    Google Scholar 

  11. Titchmarsh, E.C., Eigenfunction expansions, Part II, Chapter XVI, Oxford University Press London, 1958.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J. B. McLeod

This work was supported by the National Science Foundation under Grant MPS-74-06835-A01.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fife, P.C., Peletier, L.A. Nonlinear diffusion in population genetics. Arch. Rational Mech. Anal. 64, 93–109 (1977). https://doi.org/10.1007/BF00280092

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00280092

Keywords

Navigation