The Freidlin–Gärtner formula for general reaction terms

Abstract

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–Gärtner 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; derivation of multi-tiered propagation for multistable equations.