×

Qualitative theory of the Fitz Hugh-Nagumo equations. (English) Zbl 0379.92002


MSC:

92B05 General biology and biomathematics
35K55 Nonlinear parabolic equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aronson, D.; Weinberger, H., Nonlinear diffusion in population genetics, combustion, and nerve propagation, (Springer Lecture Notes in Mathematics, No. 446 (1975), Springer-Verlag: Springer-Verlag New York) · Zbl 0325.35050
[2] Carpenter, G., A geometric approach to singular perturbation problems with applications to nerve impulse equations, J. Differential Equations, 23, 335-367 (1977) · Zbl 0341.35007
[3] Cohen, H., Nonlinear diffusion problems, (MAA Studies in Mathematics, Vol. 7 (1971), MAA), 27-64
[4] Conley, C., Traveling wave solutions of nonlinear diffusion equations, (Springer Lecture Notes in Physics, No. 38 (1975), Springer-Verlag: Springer-Verlag New York) · Zbl 0316.34063
[5] Chueh, K.; Conley, C.; Smoller, J., Positively invariant regions for systems of nonlinear parabolic equations, Ind. Univ. Math. J., 26, 373-392 (1977) · Zbl 0368.35040
[6] Courant, R.; Hilbert, D., (Methods of Mathematical Physics, Vol. I (1966), Interscience: Interscience New York) · Zbl 0729.00007
[7] Dieudonné, J., Foundations of Modern Analysis (1960), Academic Press: Academic Press New York · Zbl 0100.04201
[8] Evans, J., Nerve axon equations I, II, III, Indiana Univ. Math. J., 22, 577-593 (1972) · Zbl 0245.92004
[9] Gelfand, I. M.; Shilov, G. E., (Generalized Functions, Vol. 3 (1967), Academic Press: Academic Press New York) · Zbl 0355.46017
[10] Hastings, S., The existence of homoclinic and periodic orbits for Nagumo’s equation, Quart. J. Math., 27, 123-134 (1976) · Zbl 0322.92008
[11] Hastings, S., Some mathematical problems from neurobiology, AMS Monthly, 82, 881-895 (1975) · Zbl 0347.92001
[12] Hodgkin, A. L.; Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerves, J. Physiol., 117, 500-544 (1952)
[13] Weinberger, H., Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Mat. Univ. Roma, 8, 295-310 (1975) · Zbl 0312.35043
[14] Schonbek, M., Boundary value problems for the FitzHugh-Nagumo equations, (Ph.D. Thesis (1976), University of Michigan) · Zbl 0407.35024
[15] Schonbek, M., Boundary value problems for the FitzHugh-Nagumo equations, MRC Technical Summary Report (1977) · Zbl 0364.35029
[16] Rauch, J., Global existence for the FitzHugh-Nagumo equations, Comm. P. D. E., 1, 609-621 (1976) · Zbl 0341.35027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.