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Journal of Applied Mathematics
Volume 2014, Article ID 529618, 7 pages
http://dx.doi.org/10.1155/2014/529618
Research Article

Inverse Estimates for Nonhomogeneous Backward Heat Problems

1School of Science, Xi'an University of Technology, Xi'an, Shaanxi 710054, China
2State Key Laboratory of Eco-Hydraulic Engineering in Shaanxi, Xi'an University of Technology, Xi'an, Shaanxi 710048, China

Received 16 September 2013; Accepted 12 January 2014; Published 2 March 2014

Academic Editor: Zhong Bo Fang

Copyright © 2014 Tao Min 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

We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first Fredholm integral equation, and an algorithm of inversion is given using Tikhonov's regularization method. The genetic algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation.