IJPAM: Volume 82, No. 4 (2013)

INVERSE ESTIMATION OF THE INITIAL
CONDITION FOR THE HEAT EQUATION

Tao Min$^1$, Bei Geng$^2$, Jucheng Ren$^3$
Xi'an University of Technology
Xi'an Shaanxi, 710054, P.R. CHINA


Abstract. In this work,we investigate the inverse problem in the 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 the Tikhonov's regularization method. The Newton root-finding algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation.

Received: September 11, 2012

AMS Subject Classification: 34A55

Key Words and Phrases: backward heat conduction problem, inverse problem, regularization, integral equation, ill-posed

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DOI: 10.12732/ijpam.v82i4.7 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 4