Conservative stochastic Cahn--Hilliard equation with reflection
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.
Cite
@article{arxiv.math/0601313,
title = {Conservative stochastic Cahn--Hilliard equation with reflection},
author = {Arnaud Debussche and Lorenzo Zambotti},
journal= {arXiv preprint arXiv:math/0601313},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/009117906000000773 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)