On increased stability in the continuation of the Helmholtz equation
On increased stability in the continuation of the Helmholtz equation
复制标题
关于亥姆霍兹方程延拓稳定性的提高
DOI：
10.1088/0266-5611/23/4/019
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发表时间：
2007
期刊：
影响因子：
2.1
通讯作者：
V. Isakov
中科院分区：
文献类型：
--
作者：
D. Subbarayappa;V. Isakov
在本文中，我们给出的分析和数值证据增加稳定性的柯西问题的亥姆霍兹方程在整个域的频率是增长。这种效应取决于柯西数据给定的曲面的凸性。证明使用以前获得的估计在子域和理论的Sobolev空间：痕迹，嵌入和插值定理。通过三维数值算例说明了该理论。结果表明，即使在声学频率范围内，分辨率随频率的增加也是相当显著的。另一方面，单位球面外延拓的分辨率在下降。
In this paper, we give analytical and numerical evidence of increasing stability in the Cauchy problem for the Helmholtz equation in the whole domain when frequency is growing. This effect depends upon the convexity properties of the surface where the Cauchy data are given. Proofs use previously obtained estimates in subdomains and the theory of Sobolev spaces: traces, embedding and interpolation theorems. The theory is illustrated by three-dimensional numerical examples. The results show that even in an acoustical frequency range the increase of resolution with growing frequency is quite dramatic. On the other hand, the resolution of continuation outside a unit sphere is decreasing.