Math @ Duke

Publications [#287348] of James H. Nolen
Papers Published
 Nolen, J; Xin, J, KPP fronts in a onedimensional random drift,
Discrete and Continuous Dynamical Systems  Series B, vol. 11 no. 2
(2009),
pp. 421442, ISSN 15313492 [doi]
(last updated on 2018/07/16)
Abstract: We establish the variational principle of KolmogorovPetrovskyPiskunov (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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