Abstract
An existence proof for periodic traveling wave solutions of an equation of Nagumo is outlined. The proof begins with the analysis of a limiting case in which one set of dependent variables moves infinitely fast compared to the remainder. Singular “orbits” are defined for this limiting system and a perturbation argument using isolating blocks allows one to find actual solutions.
Sponsored by the U.S. Army under Contract No. DA-31-124-ARO-D-462.
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References
Conley, C., Hyperbolic sets and the shift automorphism, in this volume.
Carpenter, G., Thesis, University of Wisconsin, Madison.
Hastings, S., On traveling wave solutions of the Hodgkin-Huxley equations, (to appear).
Hastings, S., The existence of periodic solutions to Nagumo's equation (to appear), Quarterly Jour. of Math., September.
Hastings, S., The existence of homoclinic orbits for Nagumo's equation, (to appear).
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© 1975 Springer-Verlag
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Conley, C.C. (1975). On traveling wave solutions of nonlinear diffusion equations. In: Moser, J. (eds) Dynamical Systems, Theory and Applications. Lecture Notes in Physics, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07171-7_13
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DOI: https://doi.org/10.1007/3-540-07171-7_13
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