Tuan Nguyen Huy, Mokhtar Kirane, Long Dinh Le, Thinh Van Nguyen
Abstract:
The backward heat problem is known to be ill possed, which has lead
to the design of several regularization methods.
In this article we apply the method of filtering out the high frequencies
from the data for a parabolic equation.
First we identify two properties that if satisfied they imply the
convergence of the approximate solution to the exact solution.
Then we provide examples of filters that satisfy the two properties,
and error estimates for their approximate solutions.
We also provide numerical experiments to illustrate our results.
Submitted December 3, 2015. Published January 15, 2016.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Ill-posed problem; truncation method; heat equation; regularization.
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Tuan Nguyen Huy Applied Analysis Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City, Vietnam email: nguyenhuytuan@tdt.edu.vn | |
Mokhtar Kirane Laboratoire de Mathematiques P&circo;le Sciences et Technologie Universié de La Rochelle Avenue M. Crépeau 17042 La Rochelle Cedex, France email: mokhtar.kirane@univ-lr.fr | |
Long Dinh Le Institute of Computational Science and Technology Ho Chi Minh City, Viet Nam email: long04011990@gmail.com | |
Thinh Van Nguyen Department of Civil and Environmental Engineering Seoul National University, Republic of Korea email: vnguyen@snu.ac.kr |
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