Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth
Volume 60 / 2012
Bulletin Polish Acad. Sci. Math. 60 (2012), 259-268
MSC: 35B41, 35K35, 76A20.
DOI: 10.4064/ba60-3-6
Abstract
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 $H^2$, which attracts all the bounded sets of $H^2$ in the $H^2$-norm.
