The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential
arXiv:1909.12106 · doi:10.1088/1361-6544/abf338
Abstract
We prove existence of martingale solutions for the stochastic Cahn-Hilliard equation with degenerate mobility and multiplicative Wiener noise. The potential is allowed to be of logarithmic or double-obstacle type. By extending to the stochastic framework a regularization procedure introduced by C. M. Elliott and H. Garcke in the deterministic setting, we show that a compatibility condition between the degeneracy of the mobility and the blow-up of the potential allows to confine some approximate solutions in the physically relevant domain. By using a suitable Lipschitz-continuity property of the noise, uniform energy and magnitude estimates are proved. The passage to the limit is then carried out by stochastic compactness arguments in a variational framework. Applications to stochastic phase-field modelling are also discussed.
arXiv comment37 pages
References in corpus (16)
- On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential
- Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics
- Conservative stochastic Cahn--Hilliard equation with reflection
- Existence and regularity of solution for a Stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion
- Global attractors for Cahn-Hilliard equations with non constant mobility
- Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections
- Stochastic Cahn-Hilliard equation with singular nonlinearity and reflection
- On the stochastic Cahn-Hilliard equation with a singular double-well potential
- Singular Stochastic Allen-Cahn equations with dynamic boundary conditions
- Optimal control of stochastic phase-field models related to tumor growth
- The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit
- Optimal distributed control of a stochastic Cahn-Hilliard equation
- Existence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditions
- From the viscous Cahn-Hilliard equation to a regularized forward-backward parabolic equation
- A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity
- Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system