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An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition

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Published/Copyright: September 21, 2017
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Abstract

The aim of this paper is to investigate the problem of control by the initial conditions of the heat equation with an integral boundary condition. Using the truncation method with an a posteriori parameter choice rule, we give the error estimate between the exact and the regularized solutions. A numerical implementation shows the efficiency of the proposed method.

Funding statement: This work is supported by Grant S08 (Sciences Fondamentales) from Directorate General for Scientific Research and Technological Development (DG-SRTD), Ministry of Higher Education and Scientific Research of Algeria.

Acknowledgements

The authors would like to express their sincere gratitude to the anonymous reviewers for their constructive comments and suggestions which improved the quality of the paper.

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Received: 2015-03-25
Revised: 2016-05-05
Accepted: 2016-07-08
Published Online: 2017-09-21
Published in Print: 2019-03-01

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