An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number

The inverse source problem of the Helmholtz equation in an interior domain is investigated. We show the uniqueness and local stability, where the source consists of multiple point sources. An algebraic algorithm is proposed to identify the number, locations and intensities of the point sources from...

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Bibliographic Details
Published in:Inverse problems 2011-10, Vol.27 (10), p.105001-15
Main Authors: Badia, Abdellatif El, Nara, Takaaki
Format: Article
Language:English
Subjects:
Boundaries
Exact sciences and technology
Helmholtz equations
Inverse
Inverse problems
Mathematical models
Physics
Point sources
Pollution sources
Uniqueness
Wavelengths
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Summary:The inverse source problem of the Helmholtz equation in an interior domain is investigated. We show the uniqueness and local stability, where the source consists of multiple point sources. An algebraic algorithm is proposed to identify the number, locations and intensities of the point sources from boundary measurements. Uniqueness and non-uniqueness results for some distributed sources are also established. The proposed method is verified numerically.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/27/10/105001