×

zbMATH — the first resource for mathematics

Existence and regularity for the FitzHugh-Nagumo equations with inhomogeneous boundary conditions. (English) Zbl 0712.35048
The author considers the FitzHugh-Nagumo equations which model the transmission of electrical impulses in a nerve axon. Existence and uniqueness of solutions to an initial-boundary value problem with irregular data is proved by the use of a Galerkin method. It is shown that this solution has a higher regularity if the data are smooth and satisfy compatibility conditions.
Reviewer: J.Sprekels

MSC:
35K57 Reaction-diffusion equations
92C05 Biophysics
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adams, R.A., Sobolev spaces, (1975), Academic Press New York · Zbl 0186.19101
[2] Hastings, S.P., Some mathematical problems from neurobiology, Am. math. mon., 82, 881-895, (1975) · Zbl 0347.92001
[3] Jerome, J.W., Convergence of successive iterative semidiscretizations for Fitzhugh-Nagumo reaction diffusion systems, S.I.A.M. J. numer. analysis, 17, 192-206, (1980) · Zbl 0434.65095
[4] Lions, J.L., Quelques methodes de resolution des problem aux limits non lineaires, (1969), Dunod Gauthier-Villars Paris · Zbl 0189.40603
[5] Lions, J.L.; Magenes, E., Non-homogeneous boundary value problems and applications, Vol. I, (1972), Springer New York · Zbl 0223.35039
[6] Lions, J.L.; Magenes, E., Non-homogeneous boundary value problems and applications, Vol. II, (1972), Springer New York · Zbl 0223.35039
[7] Peskin, Partial differential equations in biology, (1975), Courant Institute of Mathematical Sciences New York · Zbl 0329.35001
[8] Rauch, J., Global existence of the Fitzhugh-Nagumo equations, Communs partial diff. eqns, 1, 609-621, (1976)
[9] Rauch, J.; Smoller, J., Qualitative theory of the Fitzhugh-Nagumo equations, Adv. math., 27, 12-44, (1978) · Zbl 0379.92002
[10] Schonbek, M.E., Boundary value problems for the hugh-Nagumo equations, J. diff. eqns, 30, 119-147, (1978) · Zbl 0407.35024
[11] Schwan, H.P., Biological engineering, (1969), McGraw-Hill New York
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.