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Existence of weak solutions for a generalized thin film equation

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


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