On strongly Petrovskii's parabolic SPDEs in arbitrary dimension and the stochastic Cahn-Hilliard equation

Abstract

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.

Cited by in corpus (4)

• On implicit and explicit discretization schemes for parabolic SPDEs in any dimension
• Spatial ergodicity for SPDEs via a Poincaré-type inequality
• Density convergence of a fully discrete finite difference method for stochastic Cahn--Hilliard equation
• Convergence analysis of a finite difference method for stochastic Cahn--Hilliard equation