On the hyperbolic relaxation of the one-dimensional Cahn–Hilliard equation ✩

We consider the one-dimensional Cahn–Hilliard equation with an inertial term εutt, for ε 0. This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup Sε(t) which acts on a suitable phase-space and possesses a global attractor. Our main result is the construction of a robust family of exponential attractors {Mε}, whose common basins of attraction are the whole phase-space.  2005 Elsevier Inc. All rights reserved