Abstract

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 \(\delta \to 0\).

中文翻译：

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双曲型方程柯西问题解的正则化

摘要

给定具有可变系数的双曲方程，我们构造了一个正则化算法来解决波场从其内部半平面的边界处连续的问题。我们介绍一些\（N \）近似解，并建立它们与精确解的收敛性。正在考虑问题数据的错误为\（\ delta \）的情况。我们找到了近似解的精确度的一个估计，并证明了该唯一解的近似解的收敛为\（\ delta \ to 0 \）。