Abstract
The FitzHugh-Nagumo equation u t = u xx + f( u)− w, w t = b( u− dw), is a simplified mathematical model of a nerve axon. If the parameters b > 0 and d > 0 are taken suitably, this equation has a travelling front solution. We study the stability of the front solution by eigenvalue analysis. It is proved analytically that the front solution is exponentially stable if b > 0 is sufficiently small.
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