Geodesic
Regularization of the solution of a Cauchy problem for a hyperbolic equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 89-102

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Given a hyperbolic equation with variable coefficients, we construct a regularizing algorithm to solve the problem of continuation of the wave field from the boundary of the half-plane inside it. We introduce some $N$-approximate solutions and establish their convergence to the exact solution. Under consideration is the case when the problem data have an error of $\delta$. We find an estimate of the accuracy of the approximate solutions and prove the convergence of the approximate solutions to the unique solution as $\delta \to 0$.
Keywords: a Cauchy problem, wave field continuation, regularization. . 
@article{SJIM_2021_24_1_a6,
     author = {V. G. Romanov and T.V. Bugueva and V. A. Dedok},
     title = {Regularization of the solution of a {Cauchy} problem for a hyperbolic equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {89--102},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a6/}
}
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V. G. Romanov; T.V. Bugueva; V. A. Dedok. Regularization of the solution of a Cauchy problem for a hyperbolic equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 89-102. http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a6/