Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle (Q2574725)

The authors consider a reaction-diffusion-advection equation with a nonlinear term that includes the Arrhenius-type nonlinearity arising in combustion and also the classical KPP (Kolmogorov-Petrovsky-Piskunov) nonlinearity. The existence of KPP travelling fronts with minimal speed is proven. For the KPP nonlinearity, the minimal front speed is characterised by a variational principle involving the principal eigenvalue of a space-time periodic parabolic operator.