We consider the one-dimensional Cahn-Hilliard equation with aninertial term ε∂_tt u, for ε ≥ 0. This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup S_ε(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 M_ε, whose common basins of attraction are the whole phase-space.
On the hyperbolic relaxation of the one-dimensional Cahn-Hilliard equation / Gatti, Stefania; Grasselli, M; Miranville, A; Pata, V.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 312:1(2005), pp. 230-247. [10.1016/j.jmaa.2005.03.029]
On the hyperbolic relaxation of the one-dimensional Cahn-Hilliard equation
GATTI, Stefania;
2005
Abstract
We consider the one-dimensional Cahn-Hilliard equation with aninertial term ε∂_tt u, for ε ≥ 0. This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup S_ε(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 M_ε, whose common basins of attraction are the whole phase-space.
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