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

• Autor(a) principal: Carmona, Sara Ianda Correa
• Data de Publicação: 1997
• Outros Autores: Tanaka, Nelson Ithiro
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/174004
• topic: Processos aleatorios : Grandes desvios : Trajetorias continuas e descontinuas; Perturbacao : Processos aleatorios; Propagação de ondas; Large deviation; Action functional; Not very large deviations; Wave front propagation

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.