An invariance principle for random traveling waves in one dimension

Journal Article

We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is either the ignition nonlinearity or the bistable nonlinearity, under suitable restrictions on the size of the spatial fluctuations. It is known that the solution develops an interface which propagates with a well-defined speed in the large time limit. The main result of this article is a functional central limit theorem for the random interface position. Copyright © 2011 by SIAM.

Full Text

Duke Authors

Cited Authors

  • Nolen, J

Published Date

  • 2011

Published In

Volume / Issue

  • 43 / 1

Start / End Page

  • 153 - 188

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/090746513