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

We consider the one-dimensional Cahn-Hilliard equation with an inertial term ɛutt, for ɛ⩾0. This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup Sɛ(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 {Mɛ}, whose common basins of attraction are the whole phase-space.