A fourth order nonlinear degenerate parabolic equation

Changchun Liu

doi:10.3934/cpaa.2008.7.617

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2008, Volume 7, Issue 3: 617-630. Doi: 10.3934/cpaa.2008.7.617

This issue Previous Article On periodic elliptic equations with gradient dependence Next Article Regularity for positive weak solutions to semi-linear elliptic equations

A fourth order nonlinear degenerate parabolic equation

Changchun Liu^1,

1.
Department of Mathematics, Jilin University, Changchun 130012

Received: February 2007

Revised: August 2007

Published online: February 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 35D05, 35K35, 35K65; Secondary: 76A20.

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