Geodesic
On the Cauchy problem for the wave equation in a two-dimensional domain with data on the boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 154-168 Cet article a éte moissonné depuis la source Math-Net.Ru

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The subject of the paper is the Cauchy problem for the wave equation in a space-time cylinder $\Omega\times{\mathbb R}$, $\Omega\subset{\mathbb R}^2$, with data on the surface $\partial\Omega\times I$, where $I$ is a finite time interval. The algorithm for solving the Cauchy problem with data on $S\times I$, $S\subset\partial\Omega$, was obtained previously. Here we adapt this algorithm to the special case $S=\partial\Omega$ and show that in this situation, the solution is determined with higher stability in comparison with the case $S\subsetneqq\partial\Omega$. 
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     author = {M. N. Demchenko},
     title = {On the {Cauchy} problem for the wave equation in a two-dimensional domain with data on the boundary},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a10/}
}
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M. N. Demchenko. On the Cauchy problem for the wave equation in a two-dimensional domain with data on the boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 154-168. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a10/

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