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Boundary layers and KPP fronts in a cellular flow. (English) Zbl 1109.76064
Summary: We study an eigenvalue problem associated with a reaction-diffusion-advection equation of KPP type in a cellular flow. We obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude \(A\gg 1\). It follows that the minimal pulsating traveling front speed \(c_{*}( A)\) satisfies the upper and lower bounds \(C_{1} A^{1/4}\leqq c_{*}( A)\leqq C_{2}A^{1/4}\). 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.

MSC:
76V05 Reaction effects in flows
35Q35 PDEs in connection with fluid mechanics
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