| Abstract: |
| In this talk, we will consider the asymptotic behavior of the stochastic Cahn-Hilliard equation with singular nonlinearity by the approach of establishing dimension-free Harnack inequalities. We mainly consider the stochastic Cahn-Hilliard equation with the singularities of the logarithmic free energy at one and minus one, and the conservation of the solution in its spatial variable. We consider both the degenerate colored noise and non-degenerate white noise. For the highly degenerate space-time colored noise, the asymptotic log-Harnack inequality is established under the so-called essentially elliptic conditions, which implies the asymptotic strong Feller property. For non-degenerate space-time white noise, the Harnack inequality with power is established. |
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