环面上外延生长问题解的解析半径
The radius of analyticity for solutions to a problem in epitaxial growth on the torus
摘要：
外延膜生长的某个模型最近引起了人们的注意，在n维环面和自由空间的情况下都证明了小的全局解的存在。我们解决这些解决方案的规律性问题，表明在环面的情况下，解决方案成为解析在任何积极的时间，与半径的解析性线性增长的所有时间。与其他作者一样，我们将初始数据的拉普拉斯算子置于维纳代数中，并且我们发现数据大小的显式小条件。我们在环面上的特殊条件是初始数据的拉普拉斯算子在维纳代数中的范数应小于小于1/4。
英文摘要：
A certain model for epitaxial film growth has recently attracted attention, with the existence of small global solutions having being proved in both the case of the n-dimensional torus and free space. We address a regularity question for these solutions, showing that in the case of the torus, the solutions become analytic at any positive time, with the radius of analyticity growing linearly for all time. As other authors have, we take the Laplacian of the initial data to be in the Wiener algebra, and we find an explicit smallness condition on the size of the data. Our particular condition on the torus is that the Laplacian of the initial data should have norm less than 1/4 in the Wiener algebra.
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