Asymptotic properties of stochastic Cahn-Hilliard equation with singular nonlinearity and degenerate noise

Abstract

We consider a stochastic partial differential equation with a logarithmic nonlinearity with singularities at $1$ and $-1$ and a constraint of conservation of the space average. The equation, driven by a trace-class space-time noise, contains a bi-Laplacian in the drift. We obtain existence of solution for equation with polynomial approximation of the nonlinearity. Tightness of this approximated sequence of solutions is proved, leading to a limit transition semi-group. We study the asymptotic properties of this semi-group, showing the existence and uniqueness of invariant measure, asymptotic strong Feller property and topological irreducibility.

References in corpus (1)

• Hitting properties of parabolic s.p.d.e.'s with reflection

Cited by in corpus (2)

• Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises
• Central limit theorem and moderate deviations for a stochastic Cahn-Hilliard equation