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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 471, Pages 140–149 (Mi znsl6630)  
One dimensional inverse problem in photoacoustic. Numerical testing

D. Langemanna, A. S. Mikhaylovbc, V. S. Mikhaylovbc

a Technische Universität Braunschweig, Institut Computational Mathematics, AG PDE, Universitätsplatz 2, 38106 Braunschweig, Germany
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
c St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034, Russia
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Abstract: We consider the problem of reconstruction of Cauchy data for the wave equation in $\mathbb R^1$ by the measurements of its solution on the boundary of the finite interval. This is a one-dimensional model for the multidimensional problem of photoacoustics, which was studied in [2]. We adapt and simplify the method for one-dimensional situation and provide the results on numerical testing to see the rate of convergence and stability of the procedure. We also give some hints on how the procedure of reconstruction can be simplified in 2d and 3d cases.
Key words and phrases: inverse problem, photoacoustic, wave equation.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00099
18-01-00269
17-01-00529
Ministry of Education and Science of the Republic of Kazakhstan AP05136197
Volkswagen Foundation
Alexandr Mikhaylov was supported by RFBR 17-01-00099, 18-01-00269, Victor Mikhaylov was supported by RFBR 18-01-00269, 17-01-00529, and by the Ministry of Education and Science of Republic of Kazakhstan under grant AP05136197. We thank the Volkswagen Foundation (VolkswagenStiftung) program “Modeling, Analysis, and Approximation Theory toward application in tomography and inverse problems” for kind support and stimulating our collaboration.
Received: 01.11.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 243, Issue 5, Pages 726–733
DOI: https://doi.org/10.1007/s10958-019-04574-6
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: D. Langemann, A. S. Mikhaylov, V. S. Mikhaylov, “One dimensional inverse problem in photoacoustic. Numerical testing”, Mathematical problems in the theory of wave propagation. Part 48, Zap. Nauchn. Sem. POMI, 471, POMI, St. Petersburg, 2018, 140–149; J. Math. Sci. (N. Y.), 243:5 (2019), 726–733
Citation in format AMSBIB
\Bibitem{LanMikMik18}
\by D.~Langemann, A.~S.~Mikhaylov, V.~S.~Mikhaylov
\paper One dimensional inverse problem in photoacoustic. Numerical testing
\inbook Mathematical problems in the theory of wave propagation. Part~48
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 471
\pages 140--149
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6630}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 243
\issue 5
\pages 726--733
\crossref{https://doi.org/10.1007/s10958-019-04574-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85075119219}
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