The stability of curved fronts in a periodic shear flow

Recently, El Smaily et al. (2011) proved the existence of curved fronts in a periodic shear flow, which satisfy some “conical” conditions at infinity in the whole plane R2. In this paper, we study the stability of these curved fronts. In fact, we prove that all the curved fronts are exponentially stable provided that the initial perturbations decay exponentially with an appropriate rate in the lower cone.