Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

Stochastic Cahn-Hilliard equation with singular nonlinearity and reflection

2 Solutions of equation with a reflection measure 10 2.1 Pathwise uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Convergence of invariants measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Existence of stationary solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Convergence of the semigroup . . . . . . . . . . ....

Sharp Interface Limit for Invariant Measures of a Stochastic Allen-cahn Equation

The invariant measure of a one-dimensional Allen-Cahn equation with an additive space-time white noise is studied. This measure is absolutely continuous with respect to a Brownian bridge with a density which can be interpreted as a potential energy term. We consider the sharp interface limit in this setup. In the right scaling this corresponds to a Gibbs type measure on a growing interval with ...

Sharp-Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility

We consider the sharp interface limit of the degenerate Cahn–Hilliard equation with polynomial free energy via matched asymptotic analysis involving exponentially growing terms and multiple inner layers. With a quadratic mobility, a contribution from nonlinear, porous-medium type bulk diffusion to the normal flux condition for the interface motion appears in the limit model to the same order as...

Sharp limit of the viscous Cahn-Hilliard equation and thermodynamic consistency

Stochastic Cahn-Hilliard Equation with Double Singular Nonlinearities and Two Reflections

We consider a stochastic partial differential equation with two logarithmic nonlinearities, with two reflections at 1 and −1 and with a constraint of conservation of the space average. The equation, driven by the derivative in space of a space-time white noise, contains a bi-Laplacian in the drift. The lack of the maximum principle for the bi-Laplacian generates difficulties for the classical p...