Skip to main content

Remarks on traveling wave solutions of non-linear diffusion equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 525)

Keywords

  • Travel Wave Solution
  • Unstable Manifold
  • Rest Point
  • Hyperbolic Periodic Orbit
  • Travel Wave Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Wazewski, T., Sur un principe topologique de l’examen de l’allure Asymptotique des Integrales des equation Differentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947) pp. 279–213.

    MathSciNet  MATH  Google Scholar 

  2. Churchill, R., Isolated invariant sets in compact metric spaces, J. Diff. Eqns., 12 (1972), 330–352.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Wilson, F. and J. Yorke, Lyapounov functions and isolating blocks, J. Diff. Eqns., 13 (1973), 106–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Conley, C. and R. Easton, On isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc., 158 (1971), 35–61.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Montgomery, J. T., Cohomology of isolated invariant sets under perturbation, J. Diff. Eqns., 13 (1973), 257–299.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Carpenter, G.A., Thesis, University of Wisconsin, 1974.

    Google Scholar 

  7. Brayton, R.K., Non-linear reciprocal networks, I.B.M. R.C. 2606, I.B.M. thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598.

    Google Scholar 

  8. Brayton, R.K., and J.K. Moser, A Theory of nonlinear networks—I; Quarterly of Applied Mathematics, Vol. XXII, No. 1, April, 1964.

    Google Scholar 

    Google Scholar 

  9. Hastings, S., The existence of periodic solutions to Nagumo’s equation, Quarterly Jour. of Math., Vol. 25, No. 99, September, 1974.

    Google Scholar 

    Google Scholar 

  10. Hastings, S., The existence of homoclinic orbits for Nagumo’s equation

    Google Scholar 

  11. Conley, C., On traveling wave solutions of non-linear diffusion equations, Lecture Notes in Physics, Dynamical Systems, Theory and Applications (Ed. J. Moser) Springer-Verlag, Berlin, Heidelberg, New York.

    Google Scholar 

  12. Conley, C., On traveling wave solutions of the Nagumo equation (unpublished).

    Google Scholar 

Related References

  1. Evans, J.W., Nerve axon equations II stability at rest, Indiana Univ. Math. J., 22 (1972), 75–90.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Fitzhugh, R., Impulses and physiological states in theoretical models of nerve membrane, Biophys. J., 1 (1961), 445–466.

    CrossRef  Google Scholar 

  3. Hodgekin, A.L., and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerves, J. Physiol., 117 (1952), 500–544.

    CrossRef  Google Scholar 

  4. Nagumo, J., S. Arimoto and S. Ycshizawa, An active pulse transmissicn line simulating nerve exon, Proc. I.R.E., 50 (1964), 2061–2070.

    CrossRef  Google Scholar 

  5. Rauch, J., and J.A. Smoller, Qualitative theory of the Fitzhugh-Nagumo equations, (to appear).

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Conley, C., Smoller, J. (1976). Remarks on traveling wave solutions of non-linear diffusion equations. In: Hilton, P. (eds) Structural Stability, the Theory of Catastrophes, and Applications in the Sciences. Lecture Notes in Mathematics, vol 525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077844

Download citation

  • DOI: https://doi.org/10.1007/BFb0077844

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07791-6

  • Online ISBN: 978-3-540-38254-6

  • eBook Packages: Springer Book Archive