TY - JOUR

T1 - Regularization of the Solution of a Cauchy Problem for a Hyperbolic Equation

AU - Romanov, V. G.

AU - Bugueva, T. V.

AU - Dedok, V. A.

N1 - Funding Information: The authors were supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0011). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2

Y1 - 2021/2

N2 - Given a hyperbolic equation with variable coefficients, we construct a regularizingalgorithm to solve the problem of continuation of the wave field from the boundary of thehalf-plane inside it. We introduce some N-approximatesolutions and establish their convergence to the exact solution. Under consideration is the casewhen the problem data have an error of δ. We find anestimate of the accuracy of the approximate solutions and prove the convergence of theapproximate solutions to the unique solution as δ→0.

AB - Given a hyperbolic equation with variable coefficients, we construct a regularizingalgorithm to solve the problem of continuation of the wave field from the boundary of thehalf-plane inside it. We introduce some N-approximatesolutions and establish their convergence to the exact solution. Under consideration is the casewhen the problem data have an error of δ. We find anestimate of the accuracy of the approximate solutions and prove the convergence of theapproximate solutions to the unique solution as δ→0.

KW - a Cauchy problem

KW - regularization

KW - wave field continuation

UR - http://www.scopus.com/inward/record.url?scp=85104703343&partnerID=8YFLogxK

U2 - 10.1134/S1990478921010105

DO - 10.1134/S1990478921010105

M3 - Article

AN - SCOPUS:85104703343

VL - 15

SP - 118

EP - 128

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -