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.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering