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