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A threshold for a caricature of the nerve equation
Author(s):
H. P.
McKean;
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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Additional information
References:
- H. Cohen, Mathematical developments in Hodgkin-Huxley theory and its approximations, Lectures Math. Life Sci., Vol. 8, Amer. Math. Soc., Providence, R.I., 1976, pp. 89-124. MR 469315
- J. Feroe, Travelling waves of infinitely many pulses in nerve equations, Math. Biosci. 55 (1981), 189-203. MR 627953
- P. Fife and J. McLeod, The approach of solutions of non-linear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977), 335-361. MR 442480
- 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. Hadeler, Non-linear diffusion equations in biology, Lect. Notes in Math. 564 (1976), 163-206. MR 526382
- 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, Nagumo's equation, Adv. in Math. 4 (1970), 209-223. MR 260438
- H. P. McKean, Stabilization of solutions of a caricature of the Fitzhugh-Nagumo equation, Comm. Pure Appl. Math. 36 (1983), 291-324; ibid. 37 (1984), 299-301. MR 739922
- J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50 (1964), 2061-2070.
- J. Rinzel, Simple equations for active nerve condition and passive neuronal integration, Lectures Math. Life Sci., Vol. 8, Amer. Math. Soc., Providence, R.I., 1976, pp. 125-164. MR 469324
- D. Terman, Threshold phenomena for a reaction-diffusion system, J. Differential Equations 47 (1983), 406-443. MR 692838
- D. Terman, A free-boundary problem arising from a bi-stable reaction-diffusion equation, SIAM J. Math. Anal. 14 (1983), 1107-1129. MR 718812
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Additional Information:
DOI:
10.1090/S0273-0979-1985-15367-4
PII:
S 0273-0979(1985)15367-4
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