Electron. J. Diff. Equ., Vol. 2016 (2016), No. 24, pp. 1-13.

Filter regularization for an inverse parabolic problem in several variables

Tuan Nguyen Huy, Mokhtar Kirane, Long Dinh Le, Thinh Van Nguyen

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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