Dang Duc Trong, Nguyen Huy Tuan
Abstract:
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 email: ddtrong@mathdep.hcmuns.edu.vn | |
Nguyen Huy Tuan Department of Information Technology and Mathematics Ton Duc Thang University 98 Ngo Tat To, Hochiminh City, Vietnam email: tuanhuy_bs@yahoo.com |
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