Journal of Applied Mathematics

The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

Xiao-Xiao Li, Fan Yang, Jie Liu, and Lan Wang

Full-text: Open access

Abstract

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 245963, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807953

Digital Object Identifier
doi:10.1155/2013/245963

Mathematical Reviews number (MathSciNet)
MR3049427

Zentralblatt MATH identifier
1266.35144

Citation

Li, Xiao-Xiao; Yang, Fan; Liu, Jie; Wang, Lan. The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation. J. Appl. Math. 2013 (2013), Article ID 245963, 8 pages. doi:10.1155/2013/245963. https://projecteuclid.org/euclid.jam/1394807953


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