The FitzHugh-Nagumo equation ut = uxx+f(u)-w,wt = 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. © 1989.
Yanagida, E. (1989). Stability of travelling front solutions of the Fitzhugh-Nagumo equations. Mathematical and Computer Modelling, 12(3), 289–301. https://doi.org/10.1016/0895-7177(89)90106-4