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Reconstructing the wave speed and the source
  • Amin Boumenir,
  • Vu Kim Tuan
Amin Boumenir
University of West Georgia

Corresponding Author:[email protected]

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Vu Kim Tuan
University of West Georgia
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Abstract

We are concerned with the inverse problem of recovering the unknown wave speed and also the source in a multidimensional wave equation. We show that the wave speed coefficient can be reconstructed from the observations of the solution taken at a single point. For the source, we may need a sequence of observation points due to the presence of multiple spectrum and nodal lines. This new method, based on spectral estimation techniques, leads to a simple procedure that delivers both uniqueness and reconstruction of the coefficients at the same time.
21 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
21 Apr 2021Submission Checks Completed
21 Apr 2021Assigned to Editor
24 Apr 2021Reviewer(s) Assigned
14 Jul 2021Review(s) Completed, Editorial Evaluation Pending
15 Jul 2021Editorial Decision: Revise Minor
18 Jul 20211st Revision Received
18 Jul 2021Submission Checks Completed
18 Jul 2021Assigned to Editor
19 Jul 2021Review(s) Completed, Editorial Evaluation Pending
19 Jul 2021Editorial Decision: Accept
Dec 2021Published in Mathematical Methods in the Applied Sciences volume 44 issue 18 on pages 14470-14480. 10.1002/mma.7713