On a generalized Cahn--Hilliard model with $p$-Laplacian

On a Generalized Cahn-hilliard Equation with Biological Applications

In this paper, we are interested in the study of the asymptotic behavior of a generalization of the Cahn-Hilliard equation with a proliferation term and endowed with Neumann boundary conditions. Such a model has, in particular, applications in biology. We show that either the average of the local density of cells is bounded, in which case we have a global in time solution, or the solution blows...

Generalized Cahn-hilliard Equations Based on a Microforce Balance

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...

On Cahn-hilliard Systems with Elasticity

A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity

We consider a generalisation of the Cahn–Hilliard equation that incorporates an elastic energy density which, being quasiconvex, incorporates microstructure formation on smaller length scales. We prove global existence of weak solutions in certain microstructural regimes in (one and) two dimensions and present sufficient conditions for uniqueness. Preliminary numerical computations to illustrat...

On linear schemes for a Cahn-Hilliard diffuse interface model

The study of interfacial dynamics in the mixture of different fluids, solids, or gas is one of the fundamental issues in hydrodynamics and materials science due it plays an increasingly important role in many current scientific, engineering, and industrial applications. Traditional fluid dynamics treats these mixtures as sharp interfaces on which a set of interfacial balance conditions must be ...