Dang Duc Trong, Nguyen Huy Tuan
The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature on the surface. We consider the problem of finding, from the final data , the initial data of the temperature function , , satisfying the nonlinear system
This problem is known to be ill-posed, as the solution exhibits unstable dependence on the given data functions. Using the Fourier series method, we regularize the problem and to get some new error estimates. A numerical experiment is given.
Submitted December 11, 2008. Published June 16, 2009.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Backward heat problem; nonlinearly ill-posed problem; Fourier series; contraction principle.
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| Dang Duc Trong |
Department of Mathematics and Informatics
Hochiminh City National University
227 Nguyen Van Cu, Q. 5, Hochiminh City, Vietnam
| Nguyen Huy Tuan |
Department of Information Technology and Mathematics
Ton Duc Thang University
98 Ngo Tat To, Hochiminh City, Vietnam
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