On a backward heat problem with time-dependent coefficient: Regularization and error estimates

In this paper, we consider a homogeneous backward heat conduction problem which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the final data. A new regularization method is applied to formulate regularized so...

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Published inApplied mathematics and computation Vol. 219; no. 11; pp. 6066 - 6073
Main Authors Nguyen Huy, Tuan, Pham Hoang, Quan, Dang Duc, Trong, Le Minh, Triet
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2013
Subjects
Backward problem
Computation
Conduction
Errors
Estimates
Fourier transform
Heat conduction
Heat equation
Heat transfer
Ill-posed problems
Mathematical models
Regularization
Time-dependent coefficient
Time-dependent coefficient
Fourier transform
Ill-posed problems
Heat equation
Backward problem
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ISSN0096-3003
1873-5649
DOI10.1016/j.amc.2012.11.069

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Summary:In this paper, we consider a homogeneous backward heat conduction problem which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the final data. A new regularization method is applied to formulate regularized solutions which are stably convergent to the exact ones with Holder estimates. A numerical example shows that the computational effect of the method is all satisfactory.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2012.11.069