A central limit theorem for pulled fronts in a random medium

James Nolen

doi:10.3934/nhm.2011.6.167

Article Contents

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

James Nolen^1,

1.
Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320

Received: August 2010

Revised: February 2011

Published: June 2011

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Abstract

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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Mathematics Subject Classification: Primary: 35R60; Secondary: 35K57, 60H99.

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