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May  2008, 7(3): 617-630. doi: 10.3934/cpaa.2008.7.617

A fourth order nonlinear degenerate parabolic equation

Changchun Liu 1,

1. 

Department of Mathematics, Jilin University, Changchun 130012, China

Received  February 2007 Revised  August 2007 Published  February 2008

In this paper, we study a fourth order degenerate parabolic equation, which arises in epitaxial growth of nanoscale thin films. We establish the existence of weak solutions, based on the uniform estimates for the approximate solutions. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.
Keywords: existence, degenerate parabolic equation, Fourth order, finite speed of propagation..
Mathematics Subject Classification: Primary: 35D05, 35K35, 35K65; Secondary: 76A2.
Citation: Changchun Liu. A fourth order nonlinear degenerate parabolic equation. Communications on Pure & Applied Analysis, 2008, 7 (3) : 617-630. doi: 10.3934/cpaa.2008.7.617
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