Global attractor for the perturbed viscous Cahn–Hilliard 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...

Attractor for a Viscous Coupled Camassa-Holm Equation

The Global Attractor Associated with the Viscous Lake Equations

We consider the motion of an incompressible fluid confined to a shallow basin with varying bottom topography. A two-dimensional shallow water model has been derived from a three-dimensional anisotropic eddy viscosity model and has been shown to be globally well posed in [15]. The dynamical system associated with the shallow water model is studied. We show that this system possesses a global att...

Spatial Analyticity on the Global Attractor for the KuramotoSivashinsky Equation

For the Kuramoto Sivashinsky equation with L-periodic boundary conditions we show that the radius of space analyticity on the global attractor is lowersemicontinuous function at the stationary solutions, and thereby deduce the existence of a neighborhood in the global attractor of the set of all stationary solutions in which the radius of analyticity is independent of the bifurcation parameter ...