the existence of global attractor for a cahn-hilliard/allen-cahn‎ ‎equation

The existence of global attractor for a Cahn-Hilliard/Allen-Cahn‎ ‎equation

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

The Viscous Cahn-hilliard Equation: Morse Decomposition and Structure of the Global Attractor

In this paper we establish a Morse decomposition of the stationary solutions of the one-dimensional viscous Cahn–Hilliard equation by explicit energy calculations. Strong non-degeneracy of the stationary solutions is proven away from turning points and points of bifurcation from the homogeneous state and the dimension of the unstable manifold is calculated for all stationary states. In the unst...

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

The convective Cahn-Hilliard equation

We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an infinite dimensional dynamical system and establish the existence of a compact attractor and a finite dimensional inertial manifold that contains it. Moreover, Gevrey regularity of solutions on the attractor is established and used to prove that four nodes are determining for each solution on the attractor...

A Generalization of the Allen-cahn Equation

Our aim in this paper is to study generalizations of the Allen-Cahn equation based on a modification of the Ginzburg-Landau free energy proposed in [25]. In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence ...