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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Stability of the travelling wave solution of the FitzHugh-Nagumo system
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by Christopher K. R. T. Jones PDF
Trans. Amer. Math. Soc. 286 (1984), 431-469 Request permission

Abstract:

Travelling wave solutions for the FitzHugh-Nagumo equations have been proved to exist, by various authors, close to a certain singular limit of the equations. In this paper it is proved that these waves are stable relative to the full system of partial differential equations; that is, initial values near (in the sup norm) to the travelling wave lead to solutions that decay to some translate of the wave in time. The technique used is the linearised stability criterion; the framework for its use in this context has been given by Evans [6-9]. The search for the spectrum leads to systems of linear ordinary differential equations. The proof uses dynamical systems arguments to analyse these close to the singular limit.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 286 (1984), 431-469
  • MSC: Primary 35B35; Secondary 35K55, 92A09
  • DOI: https://doi.org/10.1090/S0002-9947-1984-0760971-6
  • MathSciNet review: 760971