 1391 Gianni Arioli, Hans Koch
 Existence and stability of traveling pulse solutions
of the FitzHughNagumo equation
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Nov 27, 13

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Abstract. The FitzHughNagumo model is a reactiondiffusion equation
describing the propagation of electrical signals
in nerve axons and other biological tissues.
One of the model parameters is the ratio ε of two time scales,
which takes values between <i>0.001</i> and <i>0.1</i> in typical simulations
of nerve axons.
Based on the existence of a (singular) limit at ε<i>=0</i>,
it has been shown that the FitzHughNagumo equation admits
a stable traveling pulse solution for sufficiently small ε<i>>0</i>.
In this paper we prove the existence of such a solution for ε<i>=0.01</i>.
We consider both circular axons and axons of infinite length.
Our method is nonperturbative and should apply
to a wide range of other parameter values.
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