Stability of traveling waves for degenerate systems of reaction diffusion equations Anna GhazaryanY. LatushkinStephen Schecter 47D0635K5735B40frontpulsespectrally stablelinearly stable$C_0$-semigroupexponential dichotomyGreiner Spectral Mapping TheoremFitzhugh-Nagumo For the linearization of a degenerate reaction-diffusion system at a traveling pulse or front, we prove a theorem that allows one to derive information about the semigroup generated by the linear operator from spectral information about the linear operator itself. The result is used to complete existing proofs of stability of traveling fronts for the Fitzhugh-Nagumo equation. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4069 10.1512/iumj.2011.60.4069 en Indiana Univ. Math. J. 60 (2011) 443 - 472 state-of-the-art mathematics http://iumj.org/access/