Some properties of solutions for a parabolic equation modeling epitaxial thin film growth

摘要

In this paper, we study a fourth-order parabolic equation with Dirichlet boundary which arises in epitaxial growth of nanoscale thin films. We proved the equation with condition p is an element of(7/4, 2), gamma not equal 0 possesses a global attractor in H-k (0 <= k <= 4), which attracts any bounded subset of Hk(Omega) in the Hk-norm. In addition to this, we consider the equation under the conditions p > 2, gamma > 0 is blow-up.