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

Ludovic Goudenège and Luigi Manca

Stochastic Processes and their Applications, 2015, vol. 125, issue 10, 3785-3800

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 sequence of approximations 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.

Keywords: Ergodicity; Cahn–Hilliard; Stochastic partial differential equations; Singular nonlinearity; Degenerate noise (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2015.05.006

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