Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
Abstract
We study a th order PDE with a nd order correction that is a modification of one suggested by Peter Smereka using the tools of Krug et al (Z. Phys. B., 1994). First, we provide a non-rigorous derivation of the full model derived with a quadratic interaction potential using the rates and methods of the last author with Jonathan Weare (PRE, 2013). Then, we prove the existence of a global in time weak solution by regularizing the equation in a way that allows us to apply the tools of Bernis-Friedman (JDE, 1990). The methods developed here can be applied to a large number of th order degenerate models. In an appendix, we also discuss the global smooth solution with small data in the Weiner algebra framework following recent developments using tools of the second author with Robert Strain (IFB, 2018).
Keywords
Cite
@article{arxiv.1905.00179,
title = {Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects},
author = {Yuan Gao and Jian-Guo Liu and Jianfeng Lu and Jeremy L. Marzuola},
journal= {arXiv preprint arXiv:1905.00179},
year = {2022}
}
Comments
Dedicated to the memory of Peter Smereka. 31 pages, 1 figure, comments welcome! References updated, comments from referee report included