Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 904183, 22 pages
Research Article

Wavelet-Galerkin Method for Identifying an Unknown Source Term in a Heat Equation

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 17 August 2011; Accepted 16 October 2011

Academic Editor: Victoria Vampa

Copyright © 2012 Fangfang Dou. 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.


We consider the problem of identification of the unknown source in a heat equation. The problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data. Meyer wavelets have the property that their Fourier transform has compact support. Therefore, by expanding the data and the solution in the basis of the Meyer wavelets, high-frequency components can be filtered away. Under the additional assumptions concerning the smoothness of the solution, we discuss the stability and convergence of a wavelet-Galerkin method for the source identification problem. Numerical examples are presented to verify the efficiency and accuracy of the method.