Boundary layers and KPP fronts in a cellular flow

We study an eigenvalue problem associated with a reaction-diffusion- advection equation of the KPP type in a cellular flow. We obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude A ≫ 1. It follows that the minimal pulsating traveling front speed c_*(A) satisfies the upper and lower bounds C ₁ A ^1/4 ≤ c _*(A)≤ C ₂ A ^1/4. Physically, the speed enhancement is related to the boundary layer structure of the associated eigenfunction - accordingly, we establish an "averaging along the streamlines" principle for the unique positive eigenfunction.