Publisher Summary This chapter focuses on the Cahn–Hilliard equation. In the context of the
Cahn–Hilliard equation, the two components could refer, for example, to a system with two …

This article studies the problem for optimal control of the convective Cahn–Hilliard equation
in one-space dimension. The optimal control under boundary condition is given, the …

By studying the coarsening dynamics of a one-dimensional spin-1 Bose-Hubbard model in a
superfluid regime, we analytically find an unconventional universal dynamical scaling for the …

A higher order convective Cahn--Hilliard-type equation that describes the faceting of a
growing surface is considered with periodic boundary conditions. By using a Galerkin …

A nonlinear evolutionary partial differential equation is considered that is obtained as a
natural (from the physical point of view) generalization of the well-known Cahn–Hilliard …

It is known that similar physical systems can reveal two quite different ways of behavior,
either coarsening, which creates a uniform state or a large-scale structure, or formation of …

In this paper, we study the existence of weak solutions for the convective Cahn–Hilliard
equation with degenerate mobility. Based on the Schauder type estimates, we establish the …

In this paper, we give exact solutions for the convective viscous Cahn--Hilliard equation.
This equation with a general symmetric double-well potential and Burgers-type convective …

We study the well-known generalised version of the nonlinear Cahn–Hilliard evolution
equation, supplemented with periodic boundary conditions. We study local bifurcations in …

Abstract We consider the Cahn–Hilliard (CH) equation with a Burgers-type convective term
that is used as a model of coarsening dynamics in laterally driven phase-separating …