Skip to main content
SpringerLink
Log in

Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation

  • Conference paper
  • First Online:
Partial Differential Equations and Related Topics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 446))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. ARONSON, D.G. and WEINBERGER, H.F., Asymptotic properties of nonlinear diffusion, (in preparation).

    Google Scholar 

  2. COHEN, H., Nonlinear diffusion problems, Studies in Mathematics 7, Studies in Applied Mathematics, ed. A. Taub. Math. Assoc. of America and Prentice Hall, (Englewood Cliffs, N. J.) 1971, 27–63.

    Google Scholar 

  3. FRIEDMAN, A. Partial Differential Equations of Parabolic Type, Prentice Hall, (Englewood Cliffs, N. J.) 1964.

    MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  5. GELFAND, I. M., Some problems in the theory of quasilinear equations, Uspekhi Mat. Nauk (N. S.) 14 (1959), 87–158; American Math. Soc. Transl. (2) 29 (1963), 295–381.

    Google Scholar 

  6. HODGKIN, A. L. and HUXLEY, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952), 500–544.

    Article  Google Scholar 

  7. 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. 132 (1961), 268–271; Soviet Math. Dokl. 1, 533–536.

    MathSciNet  Google Scholar 

  8. KANEL', JA. I., Certain problems on equations in the theory of burning, Dokl. Akad. Nauk S.S.S.R. 136 (1961), 277–280; Soviet Math. Dokl. 2, 48–51.

    MathSciNet  Google Scholar 

  9. KANEL', JA. I., Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory, Mat. Sbornik (N. S.) 59 (101) (1962), supplement, 245–288.

    MathSciNet  Google Scholar 

  10. KANEL', JA. I., On the stability of solutions of the equation of combustion theory for finite initial functions, Mat. Sbor. (N. S.) 65 (107) (1964) 398–413.

    MathSciNet  Google Scholar 

  11. KOLMOGOROFF, A., PETROVSKY, I., and PISCOUNOFF, N., Étude 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.

    MATH  Google Scholar 

  12. NAGUMO, J., ARIMOTO, S., and YOSHIZAWA, S., An active pulse transmission line simulating nerve axon, Proc. Inst. of Radio Eng. 50 (1962), 2061–2070.

    Google Scholar 

  13. NAGUMO, J., YOSHIZAWA, S., and ARIMOTO, S., Bistable transmission lines, I. E. E. E. Transactions on Circuit Theory 12 (1965), 400–412.

    Article  Google Scholar 

  14. PROTTER, M. H. and WEINBERGER, H. F., Maximum Principles in Differential Equations, Prentice Hall (Englewood Cliffs, N. J.) 1967.

    MATH  Google Scholar 

  15. PETROVSKI, I. G., Ordinary Differential Equations, Prentice-Hall (Englewood Cliffs, N. J.) 1966, Dover (New York) 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 55455, Minneapolis, Minnesota

    D. G. Aronson & H. F. Weinberger

Authors
  1. D. G. Aronson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. F. Weinberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jerome A. Goldstein

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Aronson, D.G., Weinberger, H.F. (1975). Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In: Goldstein, J.A. (eds) Partial Differential Equations and Related Topics. Lecture Notes in Mathematics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070595

Download citation

  • DOI: https://doi.org/10.1007/BFb0070595

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07148-8

  • Online ISBN: 978-3-540-37440-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation