The problem of reconstruction of the Cauchy data for the wave equation in ℝ1 from the measurements of its solution on the boundary of a finite interval is considered. This is a one-dimensional model for the multidimensional problem of photoacoustics, which was studied previously. The method was adapted and simplified for the one-dimensional situation. The results of numerical testing to see the rate of convergence and the stability of the procedure are given. Some hints are also given on how the procedure of reconstruction can be simplified in the 2d and 3d cases.
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Dedicated to the memory of A. P. Kachalov
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 471, 2018, pp. 140–149.
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Langemann, D., Mikhaylov, A.S. & Mikhaylov, V.S. The One-Dimensional Inverse Problem in Photoacoustics. Numerical Testing. J Math Sci 243, 726–733 (2019). https://doi.org/10.1007/s10958-019-04574-6
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DOI: https://doi.org/10.1007/s10958-019-04574-6