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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

35K57 Reaction-diffusion equations
92C05 Biophysics
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
Full Text: DOI
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