Conservative stochastic Cahn-Hilliard equation with reflection. (English) Zbl 1130.60068
The authors consider a conservative stochastic Cahn-Hilliard equation with homogeneous Neumann boundary conditions and reflection at 0. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Since the maximum principle does not work for the double Laplacian, the techniques based on the penalization method break down. Then, the authors give a new approach to the equation that yields well-posedness, the study of the invariant measure and an integration by parts formula on such measures. More precisely, they obtain pathwise uniqueness, existence of stationary and strong solutions and they also study the related Dirichlet form. One of the main tools of this work is to consider an uniform strong Feller property. It seems that this new approach can be applied to some extensions of the original equation.
Reviewer: Carles Rovira (Barcelona)
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 37L40 | Invariant measures for infinite-dimensional dissipative dynamical systems |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
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