KPP fronts in a one-dimensional random drift
Journal Article
We establish the variational principle of Kolmogorov-Petrovsky-Piskunov (KPP) front speeds in a one dimensional random drift which is a mean zero stationary ergodic process with mixing property and local Lipschitz continuity. To prove the variational principle, we use the path integral representation of solutions, hitting time and large deviation estimates of the associated stochastic flows. The variational principle allows us to derive upper and lower bounds of the front speeds which decay according to a power law in the limit of large root mean square amplitude of the drift. This scaling law is different from that of the effective diffusion (homogenization) approximation which is valid for front speeds in incompressible periodic advection.
Full Text
Duke Authors
Cited Authors
- Nolen, J; Xin, J
Published Date
- 2009
Published In
Volume / Issue
- 11 / 2
Start / End Page
- 421 - 442
International Standard Serial Number (ISSN)
- 1531-3492
Digital Object Identifier (DOI)
- 10.3934/dcdsb.2009.11.421