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