论文标题
针对外延生长的连续模型的解决方案的规律性和单调性，非局部弹性效应
Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects
论文作者
论文摘要
我们研究了从结晶材料上外延生长衍生的非局部第四阶退化方程。我们首先证明了使用梯度流结构使用一般初始数据的演化变化不平等解决方案的全局存在。然后，有了单调的初始数据，我们证明了相关凸功能的细分差异确实是单价值的，这给出了较高的全局解决方案的规律性。尤其是，较高的规则材料暗示着严格的单调性一直保持着，这为全球时间单调的单调解决方案提供了对外延生长模型的严格理由，并对速度表面具有非局部弹性作用。
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.
