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

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.

MSC:

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