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Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth

Ning Duan;  Xiaopeng Zhao — 2012

Bulletin of the Polish Academy of Sciences. Mathematics

This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H², which attracts all the bounded sets of H² in the H²-norm.

Global Attractor for the Convective Cahn-Hilliard Equation in H k

Xiaopeng Zhao;  Ning Duan — 2011

Bulletin of the Polish Academy of Sciences. Mathematics

We consider the convective Cahn-Hilliard equation with periodic boundary conditions. Based on the iteration technique for regularity estimates and the classical theorem on existence of a global attractor, we prove that the convective Cahn-Hilliard equation has a global attractor in H k .

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