Regularity in Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces
Regularity in Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces
复制标题
邻面弹性外延生长连续体模型弱解的时间规律性
DOI：
10.1080/03605302.2015.1045074
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发表时间：
2015
影响因子：
1.9
通讯作者：
X. Lu
中科院分区：
文献类型：
--
作者：
I. Fonseca;G. Leoni;X. Lu
由Xiang（SIAM J.Appl.Math.63：241-258，2002）导出的描述异质外延生长中的邻位表面的演化方程是（1），其中h表示膜的表面高度，并且H是希尔伯特变换。解的存在性由Dal Maso等人获得（Arch. Rational Mech. Anal. 212：1037-1064）。时间上的规律性还没有得到解决。本文的目的是证明弱解的存在性，唯一性和Lipschitz正则性的时间，适当的假设下的初始数据。
The evolution equation derived by Xiang (SIAM J. Appl. Math. 63:241–258, 2002) to describe vicinal surfaces in heteroepitaxial growth is (1) where h denotes the surface height of the film, and H is the Hilbert transform. Existence of solutions was obtained by Dal Maso et al. (Arch. Rational Mech. Anal. 212: 1037–1064). The regularity in time was left unresolved. The aim of this paper is to prove existence, uniqueness, and Lipschitz regularity in time for weak solutions, under suitable assumptions on the initial datum.