Exponential estimates for "not very large deviations" and wave front propagation for class of reaction-diffusion equations

Abstract

A Large Deviation Principle for a class of ranclom processes depending on a small parameter ε > O is established. This class of processes arises from a random perturbation of a dynamical system. Then, exponential estimates for events of the type "not very large deviations" (deviations of εκ, O < κ < 1/2) are obtained. Finally, the wave front propagation, as ε ! O, of the solution of some initial-boundary value problems is analyzed; these problems are formulated in terms of a reaction-di[fusion equation whose diffusion coefficient is of order 1/ε. and the non linear term is of order 1/ε1-2κ. The wave front is characterized in terms of the action functional corresponding to the Large Deviation Principle initially obtained.