On increased stability in the continuation of the Helmholtz equation
Aralumallige, Deepak Isakov, Victor
Aralumallige, Deepak
Isakov, Victor
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2007-08
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Deepak Aralumallige Subbarayappa and Victor Isakov. 2007. On increased stability in the continuation of the Helmholtz equation. Inverse Problems 23(4): 1689.
Abstract
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.
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IOP Publishing
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Inverse Problems;v.23
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0266-5611
1361-6420
1361-6420