The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation in systems such as alloys and other physical and chemical applications. We describe our investigation of this field equation and report on the various discretisation schemes we used to integrate the system in one-, twoand three-dimensions. We also discuss how the equation can be visualised effectiv...

multiplicity of positive solutions for a class of semilinear problem. II. Junping Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability. multiplicity of positive solutions for a class of semilinear problems. Existence and instability of spike layer solutions to singular perturbation problems. J.

The Mullins Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn Hilliard equation. We show that classical solutions exist globally and tend to spheres exponentially fast, provided that they are close to a sphere initially. Our analysis is based on center manifold theory and on maximal regularity. 1998 Academic Press

We prove an additional result on the linearized Cahn-HilliardCook equation to fill in a gap in the main argument in our paper which was published in SIAM J. Numer. Anal. 49 (2011), 2407–2429. The result is a pathwise error estimate, which is proved by an application of the factorization argument for stochastic convolutions.

We prove an additional result on the linearized Cahn-HilliardCook equation to fill in a gap in the main argument in our paper which was published in SIAM J. Numer. Anal. 49 (2011), 2407–2429. The result is a pathwise error estimate, which is proved by an application of the factorization argument for stochastic convolutions.

Abstract We investigate a Cahn-Hilliard type equation with gradient dependent potential. After establishing the existence and uniqueness, we pay our attention mainly to the regularity of weak solutions by means of the energy estimates and the theory of Campanato Spaces.

We develop an alternative method to matched asymptotic expansions for the construction of approximate solutions of the Cahn-Hilliard equation suitable for the study of its sharp interface limit. The method is based on the Hilbert expansion used in kinetic theory. Besides its relative simplicity, it leads to calculable higher order corrections to the interface motion.

The Cahn-Hilliard equation is discretized by a Galerkin finite element method based on continuous piecewise linear functions in space and discontinuous piecewise constant functions in time. A posteriori error estimates are proved by using the methodology of dual weighted residuals.

A formal asymptotic analysis of two classes of phase field models for void growth and coarsening in irradiated solids has been performed to assess their sharp-interface kinetics. It was found that the sharp interface limit of type B models, which include only point defect concentrations as order parameters governed by Cahn-Hilliard equations, captures diffusion-controlled kinetics. It was also ...

This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a time-discrete Cahn–Hilliard–Navier–Stokes system with variable densities. The free energy density associated to the Cahn-Hilliard system incorporates the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time insta...