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Volume 11, Issue 2
Solving Inverse Problems for Hyperbolic Equations via the Regularization Method

Wen-Hua Yu

J. Comp. Math., 11 (1993), pp. 142-153.

Published online: 1993-11

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  • Abstract

In the paper, we first deduce an optimization problem from an inverse problem for a general operator equation and prove that the optimization problem possesses a unique, stable solution that converges to the solution of the original inverse problem, if it exists, as a regularization factor goes to zero. Secondly, we apply the above results to an inverse problem determining the spatially varying coefficients of a second order hyperbolic equation and obtain a necessary condition, which can be used to get an approximate solution to the inverse problem.  

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@Article{JCM-11-142, author = {Yu , Wen-Hua}, title = {Solving Inverse Problems for Hyperbolic Equations via the Regularization Method}, journal = {Journal of Computational Mathematics}, year = {1993}, volume = {11}, number = {2}, pages = {142--153}, abstract = {

In the paper, we first deduce an optimization problem from an inverse problem for a general operator equation and prove that the optimization problem possesses a unique, stable solution that converges to the solution of the original inverse problem, if it exists, as a regularization factor goes to zero. Secondly, we apply the above results to an inverse problem determining the spatially varying coefficients of a second order hyperbolic equation and obtain a necessary condition, which can be used to get an approximate solution to the inverse problem.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9312.html} }
TY - JOUR T1 - Solving Inverse Problems for Hyperbolic Equations via the Regularization Method AU - Yu , Wen-Hua JO - Journal of Computational Mathematics VL - 2 SP - 142 EP - 153 PY - 1993 DA - 1993/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9312.html KW - AB -

In the paper, we first deduce an optimization problem from an inverse problem for a general operator equation and prove that the optimization problem possesses a unique, stable solution that converges to the solution of the original inverse problem, if it exists, as a regularization factor goes to zero. Secondly, we apply the above results to an inverse problem determining the spatially varying coefficients of a second order hyperbolic equation and obtain a necessary condition, which can be used to get an approximate solution to the inverse problem.  

Yu , Wen-Hua. (1993). Solving Inverse Problems for Hyperbolic Equations via the Regularization Method. Journal of Computational Mathematics. 11 (2). 142-153. doi:
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