Article ID Journal Published Year Pages File Type
5774319 Journal of Differential Equations 2017 27 Pages PDF
Abstract
We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions d≤3.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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