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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)


A threshold for a caricature of the nerve equation

Authors: H. P. McKean and V. Moll
Journal: Bull. Amer. Math. Soc. 12 (1985), 255-259
MSC (1980): Primary 35K55, 35Q20; Secondary 92A09
MathSciNet review: 776480
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  • Hirsh Cohen, Mathematical developments in Hodgkin-Huxley theory and its approximations, Some mathematical questions in biology, VII (Proc. Ninth Sympos. Math. Biol., New York, 1975) Amer.Math. Soc., Providence, R.I., 1976, pp. 89–124. Lectures on Math. in the Life Sciences, Vol. 8. MR 0469315 (57 #9108)
  • John A. Feroe, Traveling waves of infinitely many pulses in nerve equations, Math. Biosci. 55 (1981), no. 3-4, 189–203. MR 627953 (83j:92019),
  • Paul C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal. 65 (1977), no. 4, 335–361. MR 0442480 (56 #862)
  • R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1 (1961), 445-466.
  • R. Fitzhugh, Mathematical models of excitation and propagation in nerve, Biological Engineering (H. Schwan, ed.), 1969, pp. 1-85.
  • K. P. Hadeler, Nonlinear diffusion equations in biology, Ordinary and partial differential equations (Proc. Fourth Conf., Univ. Dundee, Dundee, 1976) Springer, Berlin, 1976, pp. 163–206. Lecture Notes in Math., Vol. 564. MR 0526382 (58 #26131)
  • A. L. Hodgkin, The conduction of the nervous impulse, Liverpool Univ. Press, Liverpool, 1971.
  • A. L. Hodgkin and A. F. Huxley, A qualitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952), 500-544.
  • H. P. McKean Jr., Nagumo’s equation, Advances in Math. 4 (1970), 209–223 (1970). MR 0260438 (41 #5064)
  • H. P. McKean, Stabilization of solutions of a caricature of the FitzHugh-Nagumo equation. II, Comm. Pure Appl. Math. 37 (1984), no. 3, 299–301. MR 739922 (85d:35102b),
  • J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50 (1964), 2061-2070.
  • John Rinzel, Simple model equations for active nerve conduction and passive neuronal integration, Some mathematical questions in biology, VII (Proc. Ninth Sympos. Math. Biol., New York, 1975) Amer. Math. Soc., Providence, R.I., 1976, pp. 125–164. Lectures on Math. in the Life Sciences, Vol. 8. MR 0469324 (57 #9117)
  • David Terman, Threshold phenomena for a reaction-diffusion system, J. Differential Equations 47 (1983), no. 3, 406–443. MR 692838 (84c:35064),
  • David Terman, A free boundary problem arising from a bistable reaction-diffusion equation, SIAM J. Math. Anal. 14 (1983), no. 6, 1107–1129. MR 718812 (84j:35093),

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PII: S 0273-0979(1985)15367-4

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