We propose and analyze two novel decoupled numerical schemes for solving the Cahn-HilliardStokes-Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator splitting) to decouple the phase-field (Cahn-Hilliard equation) from the velocity field (Stokes-Darcy fluid equations). To further decouple the Stokes-Darcy system...

The Cahn-Hilliard equation is very important in materials science. It is a conservation law which describes important qualitative behaviors of two-phase systems, namely, the phase separation process in a binary alloy. This phenomenon can be observed, for instance, when the alloy is cooled down sufficiently. One then observes a partial nucleation (i.e., the apparition of nucleides in the materia...

A description of the short time behavior of solutions of the Allen-Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [9] in spatial dimension n = 2 to arbitrary dimensions. Resumé On étudie le comportem...

Abstract We consider the Allen–Cahn equation $${\partial _t}{u}-\Delta u=u-u^3$$ ∂ t u - Δ = 3 with a rapidly mixing Gaussian field as init...

There has been recently an important interest in deriving rigorously the Cahn-Hilliard equation from nonlocal equation, also called aggregation equation. So far, only non-degenerate mobilities were treated. Since we are motivated by models for biomechanics of living tissues, it is useful to include degenerate mobilities. In this framework, present a new method show convergence local The include...