In this paper we show that the Cahn-Hilliard stochastic SPDE has a function valued solution in dimension 4 and 5 when the perturbation is driven by a space-correlated Gaussian noise. This is done proving general results on SPDEs with globally Lipschitz coefficients associated with operators on smooth domains of $\mathbb{R}^d$ which are parabolic in the sense of Petrovskii}, and do not necessarily define a semi-group of operators. We study the regularity of the trajectories of the solutions and the absolute continuity of the law at some given time and position.
Publié le : 2004-01-05
Classification:
Parabolic operators,
Cahn-Hilliard equation,
Green function,
SPDEs,
Malliavin calculus,
60H07 60H15 35R60,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00111189,
author = {Cardon-Weber, Caroline and Millet, Annie},
title = {On strongly Petrovskii's parabolic SPDEs in arbitrary dimension and the stochastic Cahn-Hilliard equation},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00111189}
}
Cardon-Weber, Caroline; Millet, Annie. On strongly Petrovskii's parabolic SPDEs in arbitrary dimension and the stochastic Cahn-Hilliard equation. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00111189/