Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises
arXiv:2101.05017 · doi:10.1016/j.jde.2020.04.047
Abstract
We study the asymptotic properties of the stochastic Cahn-Hilliard equation with the logarithmic free energy by establishing different dimension-free Harnack inequalities according to various kinds of noises. The main characteristics of this equation are the singularities of the logarithmic free energy at 1 and --1 and the conservation of the mass of the solution in its spatial variable. Both the space-time colored noise and the space-time white noise are considered. For the highly degenerate space-time colored noise, the asymptotic log-Harnack inequality is established under the so-called essentially elliptic conditions. And the Harnack inequality with power is established for non-degenerate space-time white noise.
References in corpus (11)
- Harnack inequality and applications for stochastic generalized porous media equations
- Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
- Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
- Harnack Inequality and Applications for Stochastic Evolution Equations with Monotone Drifts
- Conservative stochastic Cahn--Hilliard equation with reflection
- Existence and regularity of solution for a Stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion
- Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections
- Stochastic Cahn-Hilliard equation with singular nonlinearity and reflection
- Asymptotic properties of stochastic Cahn-Hilliard equation with singular nonlinearity and degenerate noise
- Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups
- Fluctuations for a conservative interface model on a wall