Properties of solutions of fourth-order nonlinear evolution equations

Abstract

In this article, we consider the existence and uniqueness of global solutions for a fourth-order nonlinear evolution equation which models the formation of facets and corners in the course of kinetically controlled crystal growth. Moreover, the existence of global attractor in $H^2$ and $H^k$ $(kgeq0)$ space is also considered.

Keywords

• Fourth-order nonlinear evolution equation
• existence
• uniqueness
• global attractor