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.

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)

References in corpus (2)

• Hitting properties of parabolic s.p.d.e.'s with reflection
• On the Brownian meander and excursion conditioned to have a fixed time average

Cited by in corpus (11)

• Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections
• Stochastic Cahn-Hilliard equation with singular nonlinearity and reflection
• On the stochastic Cahn-Hilliard equation with a singular double-well potential
• The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit
• Optimal distributed control of a stochastic Cahn-Hilliard equation
• Stochastic Allen-Cahn Equation with Logarithmic Potential
• Asymptotic properties of stochastic Cahn-Hilliard equation with singular nonlinearity and degenerate noise
• Scaling limits of weakly asymmetric interfaces
• Analysis and optimal velocity control of a stochastic convective Cahn-Hilliard equation
• Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises
• The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential