Duc Trong Dang, Huy Tuan Nguyen
Abstract:
In this article, we study the inverse time problem for the
non-homogeneous heat equation which is a severely ill-posed problem.
We regularize this problem using the quasi-reversibility method
and then obtain error estimates on the approximate solutions.
Solutions are calculated by the contraction principle
and shown in numerical experiments. We obtain also rates of
convergence to the exact solution.
Submitted November 11, 2005. Published January 11, 2006.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Backward heat problem; ill-posed problem;
contraction principle; quasi-reversibility methods.
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| Duc Trong Dang Department of Mathematics Hochiminh City National University 227 Nguyen Van Cu, Q5, HoChiMinh City, Vietnam email: ddtrong@mathdep.hcmuns.edu.vn | |
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Huy Tuan Nguyen Department of Mathematics Hochiminh City National University 227 Nguyen Van Cu, Q5, HoChiMinh City, Vietnam email: tuanhuy_bs@yahoo.com |
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