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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 109340, 9 pages
http://dx.doi.org/10.1155/2013/109340
Research Article

A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
2School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
3Department of Mathematical Sciences, Xidian University, Xi'an 710071, China

Received 12 June 2012; Revised 19 December 2012; Accepted 20 December 2012

Academic Editor: Fatih Yaman

Copyright © 2013 Zhi-Liang Deng 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

The ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed. A simple regularization method based on Dirichlet kernel mollification techniques is introduced. We also propose a priori and a posteriori parameter choice rules and get the corresponding error estimate between the exact solution and its regularized approximation. Moreover, a numerical example is provided to verify our theoretical results.