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2 Bulletin of the Polish Academy of Sciences. Mathematics

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

Duan N., Zhao X.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 3

259--268

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.

Weak solutions for a fourth order degenerate parabolic equation

Liu C., Guo J.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 1

27-39

We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.