Dynamics of domain walls governed by the convective Cahn–Hilliard equation

On a fractional step-splitting scheme for the Cahn-Hilliard equation

“…Coarsening is a major property since it is the behavior of the physical process (spinodal decomposition) that the equation models (Golovin et al, 1998;Podolny et al, 2005;Watson, 2003) as time progresses. Here we solve (see for example Eden and Kalantarov (2007)), For the conservation of mass, we have: The last equality is due to periodicity.…”

The Existence of Global Attractor for Convective Cahn-Hilliard Equation

“…By some a priori estimates, he proved the existence of a classical solution, and gave the error estimates by the discontinuous Galerkin method. A. Podolny et al [12] studied the convective Cahn-Hilliard equation with A(u) = u 3 − u and B(u) = u 2 . In their paper, the dynamics of domain walls (kinks) governed by the convective Cahn-Hilliard equation was studied by means of asymptotic and numerical methods.…”

“…M. A. Zaks et al [19] investigate bifurcations of stations periodic solutions of a convective Cahn-Hilliard equation, they described phase separation in driven systems, and studied the stability of the main family of these solutions. Eden and Kalantarov [3,4] considered the convective Cahn-Hilliard equation as [12] with periodic boundary conditions in one space dimension and three space dimension. They established some result on the existence of a compact attractor.…”

On the convective Cahn–Hilliard equation with degenerate mobility

“…(1.1) arises naturally as a continuous model for the formation of facets and corners in crystal growth (see [9,13,14]). Here u(x, t) denotes the slope of the interface.…”

“…Here u(x, t) denotes the slope of the interface. The convective term u ∂u ∂x (see [13,14]) stems from the effect of kinetics (the finite rate of atoms or molecules attachment to the crystal surface) that provides an independent flux of the order parameter, similar to the effect of an external field in spinodal decomposition of a driven system.…”