Existence of KPP type fronts in space-time periodic shear flows and a study of minimal speeds based on variational principle

Journal Article

We prove the existence of reaction-diffusion traveling fronts in mean zero space-time periodic shear flows for nonnegative reactions including the classical KPP (Kolmogorov-Petrovsky-Piskunov) nonlinearity. For the KPP nonlinearity, the minimal front speed is characterized by a variational principle involving the principal eigenvalue of a space-time periodic parabolic operator. Analysis of the variational principle shows that adding a mean-zero space time periodic shear flow to an existing mean zero space-periodic shear flow leads to speed enhancement. Computation of KPP minimal speeds is performed based on the variational principle and a spectrally accurate discretization of the principal eigenvalue problem. It shows that the enhancement is monotone decreasing in temporal shear frequency, and that the total enhancement from pure reaction-diffusion obeys quadratic and linear laws at small and large shear amplitudes.

Full Text

Duke Authors

Cited Authors

  • Nolen, J; Xin, J

Published Date

  • January 1, 2005

Published In

Volume / Issue

  • 13 / 5

Start / End Page

  • 1217 - 1234

International Standard Serial Number (ISSN)

  • 1078-0947

Digital Object Identifier (DOI)

  • 10.3934/dcds.2005.13.1217

Citation Source

  • Scopus