TY - JOUR

T1 - The One-Dimensional Inverse Problem in Photoacoustics. Numerical Testing

AU - Langemann, D.

AU - Mikhaylov, A. S.

AU - Mikhaylov, V. S.

N1 - Langemann, D., Mikhaylov, A.S. & Mikhaylov, V.S. J Math Sci (2019) 243: 726. https://doi.org/10.1007/s10958-019-04574-6

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85075119219&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/onedimensional-inverse-problem-photoacoustics-numerical-testing

U2 - 10.1007/s10958-019-04574-6

DO - 10.1007/s10958-019-04574-6

M3 - Article

AN - SCOPUS:85075119219

VL - 243

SP - 726

EP - 733

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -