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arXiv · 1412.2642

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

Ludovic Goudenège·Luigi Manca
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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.

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Ludovic Goudenège, Luigi Manca. 2014-12-08. Asymptotic properties of stochastic Cahn-Hilliard equation with singular nonlinearity and degenerate noise. https://doi.org/10.1016/j.spa.2015.05.006

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