Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 878109, 13 pages
http://dx.doi.org/10.1155/2012/878109
Research Article

A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

Jinghuai Gao,1 Dehua Wang,1 and Jigen Peng2

1Institute of Wave and Information, National Engineering Laboratory for Offshore Oil Exploration, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
2School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China

Received 30 September 2012; Revised 16 November 2012; Accepted 22 November 2012

Academic Editor: Carla Roque

Copyright © 2012 Jinghuai Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical tests are presented to illustrate the effectiveness and stability of our proposed method.