Boundary Layers and KPP Fronts in a Cellular Flow |
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Authors: | Alexei Novikov Lenya Ryzhik |
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Institution: | (1) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;(2) Department of Mathematics, University of Chicago, Chicago, IL 60637, USA |
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Abstract: | 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. |
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Keywords: | |
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