Boundary layers and KPP fronts in a cellular flow

Alexei Novikov, Lenya Ryzhik

Research output: Contribution to journalArticle

31 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)23-48
Number of pages26
JournalArchive for Rational Mechanics and Analysis
Volume184
Issue number1
DOIs
StatePublished - Apr 1 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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