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Volume 9, Issue 2
On the Relation Between an Inverse Problem for a System of Ordinary Differential Equations and an Initial Boundary Value Problem for a Hyperbolic System

Xiu-Min Shao & Zhong-Min Yuan

J. Comp. Math., 9 (1991), pp. 135-148.

Published online: 1991-09

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  • Abstract

This paper deals with a coefficient inverse problem of a system of ODEs whose coefficient matrix is the so-called generalized negative definite matrix. To solve the problem, an initial-boundary value problem of a hyperbolic system of PDEs is constructed. The existence and uniqueness of its solution and its asymptotic convergence with respect to one of the variables to the original inverse problem are proved. As a result, the solution of the inverse problem is reduced to the solution of the direct problem. A few numerical examples were solved to show the effectiveness of the method.

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@Article{JCM-9-135, author = {Shao , Xiu-Min and Yuan , Zhong-Min}, title = {On the Relation Between an Inverse Problem for a System of Ordinary Differential Equations and an Initial Boundary Value Problem for a Hyperbolic System}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {2}, pages = {135--148}, abstract = {

This paper deals with a coefficient inverse problem of a system of ODEs whose coefficient matrix is the so-called generalized negative definite matrix. To solve the problem, an initial-boundary value problem of a hyperbolic system of PDEs is constructed. The existence and uniqueness of its solution and its asymptotic convergence with respect to one of the variables to the original inverse problem are proved. As a result, the solution of the inverse problem is reduced to the solution of the direct problem. A few numerical examples were solved to show the effectiveness of the method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9386.html} }
TY - JOUR T1 - On the Relation Between an Inverse Problem for a System of Ordinary Differential Equations and an Initial Boundary Value Problem for a Hyperbolic System AU - Shao , Xiu-Min AU - Yuan , Zhong-Min JO - Journal of Computational Mathematics VL - 2 SP - 135 EP - 148 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9386.html KW - AB -

This paper deals with a coefficient inverse problem of a system of ODEs whose coefficient matrix is the so-called generalized negative definite matrix. To solve the problem, an initial-boundary value problem of a hyperbolic system of PDEs is constructed. The existence and uniqueness of its solution and its asymptotic convergence with respect to one of the variables to the original inverse problem are proved. As a result, the solution of the inverse problem is reduced to the solution of the direct problem. A few numerical examples were solved to show the effectiveness of the method.

Shao , Xiu-Min and Yuan , Zhong-Min. (1991). On the Relation Between an Inverse Problem for a System of Ordinary Differential Equations and an Initial Boundary Value Problem for a Hyperbolic System. Journal of Computational Mathematics. 9 (2). 135-148. doi:
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