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arXiv · 2004.03110

Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects

Yuan Gao·Xin Yang Lu·Chong Wang
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Abstract

We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. We first prove the global existence of evolution variational inequality solution with a general initial data using the gradient flow structure. Then with a monotone initial data, we prove the subdifferential of the associated convex functional is indeed single-valued, which gives higher regularities of the global solution. Particularly, higher regularites imply that the strict monotonicity maintains for all time, which provides rigorous justification for global-in time monotone solution to epitaxial growth model with nonlocal elastic effects on vicinal surface.

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Yuan Gao, Xin Yang Lu, Chong Wang. 2020-04-07. Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects. https://doi.org/10.1515/acv-2020-0114

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