The Freidlin-Gartner formula for general reaction terms

We devise a new geometric approach to study the propagation of disturbance - compactly supported data - in reaction diffusion equations. The method builds a bridge between the propagation of disturbance and of almost planar solutions. It applies to very general reaction-diffusion equations. The main consequences we derive in this paper are: a new proof of the classical Freidlin-Gartner formula for the asymptotic speed of spreading for periodic Fisher-KPP equations, extension of the formula to the monostable, combustion and bistable cases, existence of the asymptotic speed of spreading for equations with almost periodic temporal dependence, multilevel propagation for multistable equations.