TY - JOUR
T1 - Global attractors for singular perturbations of the Cahn-Hilliard equations
AU - Zheng, Songmu
AU - Milani, Albert
PY - 2005/2/1
Y1 - 2005/2/1
N2 - We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn-Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.
AB - We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn-Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.
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U2 - 10.1016/j.jde.2004.08.026
DO - 10.1016/j.jde.2004.08.026
M3 - Article
AN - SCOPUS:10944240024
SN - 0022-0396
VL - 209
SP - 101
EP - 139
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -