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We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure.
Maria B. Kania. "Global attractor for the perturbed viscous Cahn-Hilliard equation." Colloquium Mathematicae 109.2 (2007): 217-229. <http://eudml.org/doc/283551>.
@article{MariaB2007, abstract = {We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure.}, author = {Maria B. Kania}, journal = {Colloquium Mathematicae}, keywords = {perturbed viscous Cahn–Hilliard equation; global attractor; semigroup theory; sectorial operator}, language = {eng}, number = {2}, pages = {217-229}, title = {Global attractor for the perturbed viscous Cahn-Hilliard equation}, url = {http://eudml.org/doc/283551}, volume = {109}, year = {2007}, }
TY - JOUR AU - Maria B. Kania TI - Global attractor for the perturbed viscous Cahn-Hilliard equation JO - Colloquium Mathematicae PY - 2007 VL - 109 IS - 2 SP - 217 EP - 229 AB - We consider the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation in space dimension n ≤ 3. Applying semigroup theory, we formulate this problem as an abstract evolutionary equation with a sectorial operator in the main part. We show that the semigroup generated by this problem admits a global attractor in the phase space (H²(Ω)∩ H¹₀(Ω)) × L²(Ω) and characterize its structure. LA - eng KW - perturbed viscous Cahn–Hilliard equation; global attractor; semigroup theory; sectorial operator UR - http://eudml.org/doc/283551 ER -