TRANSITION FRONTS FOR INHOMOGENEOUS FISHER-KPP REACTIONS AND NON-LOCAL DIFFUSION

Abstract. We prove existence of and construct transition fronts for a class of reactiondiffusion equations with spatially inhomogeneous Fisher-KPP type reactions and non-local diffusion. Our approach is based on finding these solutions as perturbations of appropriate solutions to the linearization of the PDE at zero. Our work extends a method introduced by one of us to study such questions in the case of classical diffusion