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

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Published 2 September 2011 • 2011 IOP Publishing Ltd
, , Citation Abdellatif El Badia and Takaaki Nara 2011 Inverse Problems 27 105001 DOI 10.1088/0266-5611/27/10/105001

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Author affiliations

1 LMAC, University of Technology of Compiègne, Compiègne, France

2 University of Electro-Communications, Chofu-shi, Tokyo, Japan

Dates

  1. Received 15 March 2011
  2. Published

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0266-5611/27/10/105001

Abstract

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.

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10.1088/0266-5611/27/10/105001