Multidimensional stability of traveling fronts in monostable reaction-diffusion equations with complex perturbations

This paper studies the multidimensional stability of traveling fronts in monostable reaction-diffusion equations, including Ginzburg-Landau equations and Fisher-KPP equations. Eckmann andWayne (1994) showed a one-dimensional stability result of traveling fronts with speeds c a (c) 1/2 c (*) (the critical speed) under complex perturbations. In the present work, we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions (n = 2, 3), employing weighted energy methods.