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Boundary value problems for the Fitzhugh-Nagumo equations. (English) Zbl 0407.35024

MSC:
35G20 Nonlinear higher-order PDEs
35K55 Nonlinear parabolic equations
92C50 Medical applications (general)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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[1] Bers, L; John, F; Schechter, M, Partial differential equations, ()
[2] {\scK. N. Chueh, C. C. Conley, and J. A. Smoller}, Positively invariant regions for systems of nonlinear diffusion equations, to appear. · Zbl 0368.35040
[3] {\scJohn Evans}, Local stability on the nerve impulse, to appear. · Zbl 0377.92003
[4] Friedman, A, Partial differential equations of parabolic type, (1964), Prentice-Hall Englewood Cliffs, N. J · Zbl 0144.34903
[5] Hastings, S.P, Some mathematical problem from neurbiology, Amer. math. monthly, 82, 881-895, (1975) · Zbl 0347.92001
[6] Hodgkin, A.H; Huxley, A.F, A quantitative description of membrane current and its applications to conduction and excitation nerves, J. physiol, 117, 500-544, (1952)
[7] Rauch, J; Smoller, J, Qualitative theory of the Fitzhugh-Nagumo equation, Advances in math., 21, 12-44, (1978) · Zbl 0379.92002
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