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

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Duan N., Zhao X.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2012
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tom 60
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nr 3
259-268
EN
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.
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Global Attractor for the Convective Cahn-Hilliard Equation in $H^k$

100%
Zhao X., Duan N.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2011
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tom 59
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nr 1
53-64
EN
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 $H^k$.
3
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Global Attractor for the Convective Cahn-Hilliard Equation

100%
Zhao X., Liu C.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2010
|
tom 58
|
nr 2
117-127
EN
This paper is concerned with the convective Cahn-Hilliard equation. We use a classical theorem on existence of a global attractor to derive that the convective Cahn-Hilliard equation possesses a global attractor on some subset of H².
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