Abstract: In this paper we study the Cauchy problem for the 4-th order nonlinear equation ${{\partial }_{t}}h+\partial _{x}^{4}h+\partial _{x}^{2}\left( {{\left| {{\partial }_{x}}h \right|}^{\alpha }} \right)=0$ in one dimension for the initial data ${{h}_{0}}$ where $\alpha \ge 5$ and $\alpha \in \mathbb{R}$. Making use of some subtle estimates of the corresponding linear equation and the nonlinear term, Littlewood-Paley theory, two-norm method and contraction mapping principle, we get the local well-posedness result in nonhomogeneous Besov spaces.

Key words: surface growth model, Cauchy problem, well-posedness, Besov spaces, Littlewood-Paley theory