Abstract

We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or nonconvex corner or edge on their boundary must vanish there. The same holds true for smooth enough transmission eigenfunctions. The proof is based on an energy identity from the enclosure method and the construction of a new type of planar complex geometrical optics solution whose logarithm is a branch of the square root. The latter allows us to deal with nonconvex corners and edges.

Keywords

  1. inverse source problem
  2. nonradiating
  3. corner scattering
  4. complex geometrical optics
  5. interior transmission eigenfunction

MSC codes

  1. Primary
  2. 35P25
  3. 78A46; Secondary
  4. 51M20
  5. 81V80

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 6255 - 6270
ISSN (online): 1095-7154

History

Submitted: 19 April 2018
Accepted: 17 September 2018
Published online: 11 December 2018

Keywords

  1. inverse source problem
  2. nonradiating
  3. corner scattering
  4. complex geometrical optics
  5. interior transmission eigenfunction

MSC codes

  1. Primary
  2. 35P25
  3. 78A46; Secondary
  4. 51M20
  5. 81V80

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