Conservative stochastic Cahn--Hilliard equation with reflection

Details Conservative stochastic Cahn--Hilliard equation with reflection Conservative stochastic Cahn--Hilliard equation with reflection

2006-01-13

arxiv.org/abs/math/0601313v2

Annals of Probability 2007, Vol. 35, No. 5, 1706-1739

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/009117906000000773 the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000773

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.

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