Global attractor for a nonlinear model with periodic boundary value condition (Q692860)

The authors consider the partial differential equation \[ u_t = -a \Delta^2 u - \mu \nabla \cdot \left(\frac{\nabla u}{1+|\nabla u|^2}\right),\;(x,t) \in \Omega \times \mathbb{R}^{+}, \] which represents a mathematical model describing the process growing of a crystal surface. Based on the iteration technique for regularity estimates and the classical existence theorem of global attractors, the authors prove the existence of a global attractor on some affine space \(H^k\;(0\leq k<+\infty)\).