Remote Access 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
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 35K55, 35Q20, 92A09

Retrieve articles in all journals with MSC (1980): 35K55, 35Q20, 92A09

Additional Information


American Mathematical Society