Harald Garcke

On the Cahn-Hilliard equation with degenerate mobility

An existence result for the Cahn–Hilliard equation with a concentration dependent diffusional mobility is presented. In particular, the mobility is allowed to vanish when the scaled concentration takes the values

On a fourth-order degenerate parabolic equation: global entropy estimates, existence, and qualitative behavior of solutions

\pm 1

A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions

, 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.

On anisotropic order parameter models for multi-phase system and their sharp interface limits

By means of energy and entropy estimates, we prove existence and positivity results in higher space dimensions for degenerate parabolic equations of fourth order with nonnegative initial values. We discuss their asymptotic behavior for

THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

t\to \infty

A Diffuse Interface Model for Alloys with Multiple Components and Phases

and give a counterexample to uniqueness.

A parametric finite element method for fourth order geometric evolution equations

We present numerical simulations which support the formal asymptotic analysis relating a multiorder parameter Allen--Cahn system to a multiphase interface problem with curvature-dependent evolution of the interfaces and angle conditions at triple junctions. Within the gradient energy of the Allen--Cahn system, the normal to an interface between phases i and j is modeled by the irreducible representations

On the parametric finite element approximation of evolving hypersurfaces in R 3

(u_i\nabla u_j - u_j\nabla u_i)/{|u_i\nabla u_j - u_j\nabla u_i|}

Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations

, where ui and uj are the ith and jth components of the vectorial order parameter

Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix

\bu\in \rz^N