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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 27, Issue 4


Numerical solution of a source identification problem: Almost coercivity

Allaberen Ashyralyev
  • Department of Mathematics, Near East University, Nicosia, TRNC, Mersin 10, Turkey; and Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia & Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan
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/ Abdullah Said ErdoganORCID iD: https://orcid.org/0000-0002-8432-3151 / Ali Ugur Sazaklioglu
  • Department of Astronautical Engineering, University of Turkish Aeronautical Association, 06790, Ankara; and Department of Mathematics, Istanbul University, 34452, Istanbul, Turkey
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Published Online: 2018-12-05 | DOI: https://doi.org/10.1515/jiip-2017-0072


The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

Keywords: Finite difference method; inverse problem; parabolic equation; source identification problem; almost coercivity; stability

MSC 2010: 65L12; 65L09; 65L20


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About the article

Received: 2017-07-26

Revised: 2018-09-19

Accepted: 2018-11-13

Published Online: 2018-12-05

Published in Print: 2019-08-01

Funding Source: Ministry of Education and Science of the Republic of Kazakhstan

Award identifier / Grant number: BR05236656

The publication has been prepared with the support of the “RUDN University Program 5-100” and published under target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 457–468, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2017-0072.

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