June  2007, 6(2): 465-480. doi: 10.3934/cpaa.2007.6.465

Existence of weak solutions for a generalized thin film equation

1. 

Department of Mathematics, and Key Laboratory of Symbolic Computation, and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China, China

2. 

Institute of System Science, College of Sciences, Northeastern University, Shenyang 110004, China

Received  May 2006 Revised  January 2007 Published  March 2007

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.
Citation: Changchun Liu, Jingxue Yin, Juan Zhou. Existence of weak solutions for a generalized thin film equation. Communications on Pure & Applied Analysis, 2007, 6 (2) : 465-480. doi: 10.3934/cpaa.2007.6.465
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