Cahn-Hilliard stochastic equation: Existence of the solution and of its density. (English) Zbl 0995.60058

Cardon-Weber, Caroline

Bernoulli 7, No. 5, 777-816 (2001).

The study of nonlinear parabolic stochastic equations has recently been undertaken. Previous works were concerned by the Burgers stochastic equation, the present one deals with the Cahn-Hilliard stochastic equation. Existence, uniqueness and regularity of a function-valued process solution to this equation are proved when it is driven by space-time white noise with a nonlinear diffusion coefficient. Malliavin calculus is used to show existence of a density of the law of the solution when the diffusion coefficient does not vanish.

Reviewer: D.Lepingle (Orléans)

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60H07	Stochastic calculus of variations and the Malliavin calculus

Keywords:

Cahn-Hilliard equation; Malliavin calculus; stochastic partial differential equation