论文标题
底部恢复水的稳定性
The stability for an inverse problem of bottom recovering in water-waves
论文作者
论文摘要
在本文中，我们处理了一类几何反相问题，以通过对水的自由表面进行一次测量，以进行底部检测。我们在自由表面上的Neumann和/或Dirichlet数据方面发现了围绕两个不同底部之间区域的大小的上限和下边界。从一般水 - 带有侧壁的有界域中的Waves系统开始，我们设法从Neumann Operator的Dirichlet中提出了问题，因此，作为在刚性边界上具有Neumann均匀条件的有界域中的椭圆问题。然后，我们研究了Dirichlet对Neumann图的特性，并分析了所谓的尺寸估计方法。
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water--waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation.
