Inertial Manifolds for the Hyperbolic Cahn-Hilliard Equation

June 17, 2024
An inertial manifold is a positively invariant smooth finite-dimensional manifold which contains the global attractor and which attracts the trajectories at a uniform exponential rate. It follows that the infinite-dimensional dynamical system is then reduced, on the inertial manifold, to a finite system of ordinary differential equations. We will give a new proof of the existence of an inertial manifold for the hyperbolic relaxation of the Cahn-Hilliard equation. Then we will show some continuity properties of the inertial manifold, as the relaxation coefficient tends to zero.