Global attractor for the perturbed viscous Cahn–Hilliard equation

Volume 109 / 2007

Maria B. Kania Colloquium Mathematicum 109 (2007), 217-229 MSC: Primary 35L70; Secondary 35B41. DOI: 10.4064/cm109-2-4

Abstract

We consider the initial-boundary value problem for the perturbed viscous Cahn–Hilliard equation in space dimension $n\leq 3$. 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 $(H^2({\mit\Omega} )\cap H^{1}_{0}({\mit\Omega} ))\times L^2({\mit\Omega} )$ and characterize its structure.

Authors

  • Maria B. KaniaInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail

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