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TECHNICAL NOTES

Investigation of the Initial Inverse Problem in the Heat Equation

[+] Author and Article Information
Khalid Masood

Hafr Al-Batin Community College, King Fahd University of Petroleum and Minerals, P.O. Box 5087, Dhahran 31261, Saudi Arabia

F. D. Zaman

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

J. Heat Transfer 126(2), 294-296 (May 04, 2004) (3 pages) doi:10.1115/1.1666886 History: Received May 15, 2002; Revised August 14, 2003; Online May 04, 2004
Copyright © 2004 by ASME
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References

Engl, H. W., Hanke, M., and Neubauer, A., 1996, Regularization of Inverse Problems, Kluwer, Dordrecht, pp. 31–42.
Weber,  C. F., 1981, “Analysis and Solution of the Ill-Posed Problem for the Heat Conduction Problem,” Int. J. Heat Mass Transfer, 24, pp. 1783–1792.
Elden, L., 1987, Inverse and Ill-Posed Problems, Engl, H. W., and Groetsch, C. W., eds., Academic Press, Inc., pp. 345–350.
Masood,  K., Messaoudi,  S., and Zaman,  F. D., 2002, “Initial Inverse Problem in Heat Equation With Bessel Operator,” Int. J. Heat Mass Transfer, 45(14), pp. 2959–2965.
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Gratzke,  U., Kapadia,  P. D., and Dowden,  J., 1991, “Heat Conduction in High-Speed Laser Welding,” J. Appl. Phys., J. Phys. D, 24, pp. 2125–2134.
Bender, C. M., and Orszag, S. A., 1978, Advanced Mathematical Methods for Scientists and Engineers, McGraw Hill, New York, Chap. 10.
Beck, J. V., Blackwell, B., and Clair, C. A. St., 1985, Inverse Heat Conduction Problems, Wiley, New York.
Al-Khalidy,  N., 1998, “On the Solution of Parabolic and Hyperbolic Inverse Heat Conduction Problems,” Int. J. Heat Mass Transfer, 41, pp. 3731–3740.
Hansen, P. C., 1997, Rank-Deficient and Discrete Ill-Posed Problems, SIAM, Philadelphia, PA, Chap. 3.
Lions, J.-L., and Lattes, R., 1967, Méthode de Quasi-réversibilité et Applications, Dunod, Paris.
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Tikhonov, A. N., and Arsenin, V. Ya., 1977, Solution of Ill-Posed Problems, John Wiley, New York.
Moultanovsky, A. V., 2002, “Mobile HVAC System Evaporator Optimization and Cooling Capacity Estimation by Means of Inverse Problem Solution,” Inverse Problems in Engng., 10 (1), pp. 1–18.
Vasin, V. V., and Ageev, A. L., 1995, Ill-Posed Problems With a Priori Information, VSP, Utrecht.

Figures

Grahic Jump Location
The case of noisy data with SNR=50 dB, N=3,m=2,T=1, and ε=0.04. The noisy data used in the heat conduction solution (12) is represented by the dotted line and in the damped wave solution (19) by the thin solid line and the noiseless temperature by the thick solid line.
Grahic Jump Location
Response of the damped model (19) in the case of noisy data with SNR=20 dB, N=3,m=2,T=1, ε=0.07
Grahic Jump Location
Response of the classical heat model (12) in the case of noisy data with SNR=20 dB, N=3,m=2,T=1

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