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Networks and Heterogeneous Media

2011, Volume 6, Issue 2: 167-194. doi: 10.3934/nhm.2011.6.167
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A central limit theorem for pulled fronts in a random medium

  • 1.
    Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320
  • Received: 01 August 2010 Revised: 01 February 2011

  • Primary: 35R60; Secondary: 35K57, 60H99.

  • We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is the KPP type nonlinearity. For a stationary and ergodic medium, and for certain initial condition, the solution develops a moving front that has a deterministic asymptotic speed in the large time limit. The main result of this article is a central limit theorem for the position of the front, in the supercritical regime, if the medium satisfies a mixing condition.

    Citation: James Nolen. A central limit theorem for pulled fronts in a random medium[J]. Networks and Heterogeneous Media, 2011, 6(2): 167-194. doi: 10.3934/nhm.2011.6.167

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  • We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is the KPP type nonlinearity. For a stationary and ergodic medium, and for certain initial condition, the solution develops a moving front that has a deterministic asymptotic speed in the large time limit. The main result of this article is a central limit theorem for the position of the front, in the supercritical regime, if the medium satisfies a mixing condition.


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