The Cauchy problem for the wave equation in Ω × ℝ with data given on some part of the boundary ∂Ω × ℝ is considered. A reconstruction algorithm for this problem based on analytic expressions is given. This result is applicable to the problem of determining a nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 471, 2018, pp. 99–112.
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Demchenko, M.N. On the Cauchy Problem for the Wave Equation with Data on the Boundary. J Math Sci 243, 698–706 (2019). https://doi.org/10.1007/s10958-019-04571-9
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DOI: https://doi.org/10.1007/s10958-019-04571-9