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September 2007 Conservative stochastic Cahn–Hilliard equation with reflection
Arnaud Debussche, Lorenzo Zambotti
Ann. Probab. 35(5): 1706-1739 (September 2007). DOI: 10.1214/009117906000000773

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

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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

Published: September 2007
First available in Project Euclid: 5 September 2007

zbMATH: 1130.60068
MathSciNet: MR2349572
Digital Object Identifier: 10.1214/009117906000000773

Subjects:
Primary: 37L40 , 60H07 , 60H15

Keywords: integration by parts formulae , Invariant measures , Stochastic partial differential equations

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 5 • September 2007
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