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.
Publié le : 2007-09-14
Classification:
Stochastic partial differential equations,
integration by parts formulae,
invariant measures,
60H15,
60H07,
37L40
@article{1189000925,
author = {Debussche, Arnaud and Zambotti, Lorenzo},
title = {Conservative stochastic Cahn--Hilliard equation with reflection},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 1706-1739},
language = {en},
url = {http://dml.mathdoc.fr/item/1189000925}
}
Debussche, Arnaud; Zambotti, Lorenzo. Conservative stochastic Cahn–Hilliard equation with reflection. Ann. Probab., Tome 35 (2007) no. 1, pp. 1706-1739. http://gdmltest.u-ga.fr/item/1189000925/