On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

On the Cahn{hilliard Equation with Degenerate Mobility

An existence result for the Cahn{Hilliard equation with a concentration dependent diiusional mobility is presented. In particular the mobility is allowed to vanish when the scaled concentration takes the values 1 and it is shown that the solution is bounded by 1 in magnitude. Finally applications of our method to other degenerate fourth order parabolic equations are discussed.

Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential

A fully computable upper bound for the finite element approximation error of Allen– Cahn and Cahn–Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element me...

The Cahn-hilliard Equation

1. Steady states. There are many two component systems in which phase separation can be induced by rapidly cooling the system. Thus, if a two component system, which is spatially uniform at temperature T1, is rapidly cooled to a second sufficiently lower temperature T2, then the cooled system will separate into regions of higher and lower concentration. A phenomenological description of the beh...

The Cahn–Hilliard Equation

Unexpectedly Linear Behavior for the Cahn-Hilliard Equation

This paper gives theoretical results on spinodal decomposition for the CahnHillard equation. We prove a mechanism which explains why most solutions for the Cahn-Hilliard equation which start near a homogeneous equilibrium within the spinodal interval exhibit phase separation with a characteristic wavelength when exiting a ball of radius R. Namely, most solutions are driven into a region of phas...