Existence of weak solutions for a generalized thin film equation

Changchun Liu; Jingxue Yin; Juan Zhou

doi:10.3934/cpaa.2007.6.465

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2007, Volume 6, Issue 2: 465-480. Doi: 10.3934/cpaa.2007.6.465

This issue Previous Article The singularity analysis of solutions to some integral equations Next Article A result on the existence of global attractors for semigroups of closed operators

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
2.
Institute of System Science, College of Sciences, Northeastern University, Shenyang 110004

Received: May 2006

Revised: January 2007

Published: June 2007

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 35G25, 35K55, 35K65; Secondary: 76A20.

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