KPP fronts in a one-dimensional random drift
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.
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Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics