Existence of weak solutions for a generalized thin film equation
Changchun Liu Jingxue Yin Juan Zhou
Communications on Pure & Applied Analysis 2007, 6(2): 465-480 doi: 10.3934/cpaa.2007.6.465
In this paper, we consider an initial-boundary problem for a fourth-order nonlinear parabolic equations. The problem as a model shares the scaling properties of the thin film equation, or as a model arises in epitaxial growth of nanoscale thin films. Our approach lies in the combination of the energy techniques with some methods based on the framework of Campanato spaces. Based on the uniform estimates for the approximate solutions, we establish the existence of weak solutions.
keywords: existence Thin film equation Campanato space.

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