Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Cahn-Hilliard stochastic equation : existence of the solution and of its density


Code(s) de Classification MSC:

Résumé: This article is devoted to show first the existence and uniqueness of a function-valued process solution to the stochastic Cahn-Hilliard equation driven by the space-time white noise with a non-linear diffusion coefficient. Then we show that the solution is locally differentiable in the sense of the Malliavin calculus, and under some non-degeneracy condition on the diffusion coefficient that, the law of the solution is absolutely continuous with respect to Lebesgue measure.

Mots Clés: Cahn-Hilliard equation ; Green functions ; SPDEs ; Malliavin calculus

Date: 1999-12-02

Prépublication numéro: PMA-543

Revised version 2001-01-24 : PMA-543bis.dvi