An Invariance Principle for Random Traveling Waves in One Dimension

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.

• Type: Journal
• Year: 2011
• Where: SIAMMA
• Authors: James Nolen
• Keywords: Functional Central Limit Theorem, Nonlinearity, Reaction Diffusion Equation, SIAMMA 2011