In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0

in this paper, we consider a cahn-hillard/allen-cahn equation. by using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in h^k(0

In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for ...

This thesis aims to introduce and analyse a primal-dual active set strategy for solving Allen-Cahn variational inequalities. We consider the standard Allen-Cahn equation with non-local constraints and a vector-valued Allen-Cahn equation with and without non-local constraints. Existence and uniqueness results are derived in a formulation involving Lagrange multipliers for local and non-local con...

Stabilized semi-implicit spectral defect correction (SSISDC) methods are constructed for the time discretization of Allen-Cahn and Cahn-Hilliard equations. These methods are unconditionally stable, lead to simple linear system to solve at each iteration and can achieve high-order time accuracy with a few iterations in each time step. Ample numerical results are presented to demonstrate the effe...

We consider a di usive interface surface tension model under compressible ow. The equation of interest is the Cahn-Hilliard or Allen-Cahn equation with advection by a non-divergence free velocity eld. We prove that both model problems are well-posed. We are especially interested in the behavior of solutions with respect to droplet breakup phenomena. Numerical simulations of 1,2 and 3D all illus...

The viscous Cahn-Hilliard equation arises as a singular limit of the phase-field model of phase transitions. It contains both the Cahn-Hilliard and Allen-Cahn equations as particular limits. The equation is in gradient form and possesses a compact global atUactor 4 comprising heteroclinic orbits between equilibria. Two classes of wmputati0n.m described,. First heteroclinic o&its on the global a...

The viscous Cahn-Hilliard equation arises as a singular limit of the phase-eld model of phase transitions. It contains both the Cahn-Hilliard and Allen-Cahn equations as particular limits. The equation is in gradient form and possesses a compact global attractor A, comprising heteroclinic orbits between equilibria. Two classes of computation are described. First heteroclinic orbits on the globa...

In this paper, a comparison study of conservative Allen–Cahn and Cahn–Hilliard equations is presented. We consider two massconservative Allen–Cahn equations and two Cahn–Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and mo...

We propose the application of a phase-field framework for three-dimensional volume reconstruction using slice data. The proposed method is based on the Allen–Cahn and Cahn–Hilliard equations, and the algorithm consists of two steps. First, we perform image segmentation on the given raw data using a modified Allen– Cahn equation. Second, we reconstruct a three-dimensional volume using amodified ...