Geodesic
On the Cauchy problem for the wave equation with data on the boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 99-112

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We consider the Cauchy problem for the wave equation in $\Omega\times\mathbb R$ with data given on some part of the boundary $\partial\Omega\times\mathbb R$. We provide a reconstruction algorithm for this problem based on analytic expressions. Our result is applicable to the problem of determining nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery. 
@article{ZNSL_2018_471_a6,
     author = {M. N. Demchenko},
     title = {On the {Cauchy} problem for the wave equation with data on the boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {99--112},
     publisher = {mathdoc},
     volume = {471},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a6/}
}
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M. N. Demchenko. On the Cauchy problem for the wave equation with data on the boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 99-112. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a6/