Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#287348] of James H. Nolen

Papers Published

  1. Nolen, J; Xin, J, KPP fronts in a one-dimensional random drift, Discrete and Continuous Dynamical Systems Series B, vol. 11 no. 2 (2009), pp. 421-442, ISSN 1531-3492 [doi]
    (last updated on 2018/10/22)

    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.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320