Abstract
We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space–time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution. We propose a method based on infinite dimensional integration by parts formulae, obtaining existence and uniqueness of a strong solution for all continuous nonnegative initial conditions and detailed information on the associated invariant measure and Dirichlet form.
Citation
Arnaud Debussche. Lorenzo Zambotti. "Conservative stochastic Cahn–Hilliard equation with reflection." Ann. Probab. 35 (5) 1706 - 1739, September 2007. https://doi.org/10.1214/009117906000000773
Information