KPP fronts in a one-dimensional random drift
James H. Nolen, Jack X. Xin · Discrete and Continuous Dynamical Systems - B · 2008
We establish the variational principle ofKolmogorov-Petrovsky-Piskunov (KPP) front speedsin a one dimensional random drift which is a mean zero stationaryergodic process with mixing property and local Lipschitz continuity.To prove the variational principle, we use the pathintegral representation of solutions,hitting time and large deviation estimates of theassociated stochastic flows.The variational principle allows us to derive upper and lower bounds of thefront speeds which decay according to a power law in the limit of large root meansquare amplitude of the drift. This scaling law is different fromthat of the effective diffusion (homogenization) approximationwhich is valid for front speeds in incompressible periodic advection.