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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 27, Issue 4

Issues

Identification of point sources in an elliptic equation from interior measurements: Application to a seawater intrusion problem

Abdellatif El Badia
  • Corresponding author
  • Sorbonne University, University of Technology of Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne LMAC, 60205 Compiègne Cedex, France
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/ Ahmad El Hajj
  • Sorbonne University, University of Technology of Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne LMAC, 60205 Compiègne Cedex, France
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/ Mustapha Jazar / Hayat Moustafa
Published Online: 2019-04-17 | DOI: https://doi.org/10.1515/jiip-2018-0095

Abstract

This paper deals with an inverse source problem for an elliptic equation, using interior measurements. Its motivation lies in the seawater intrusion phenomenon, where we are interested in identifying point sources representing illegal wells. A cost function transforming our inverse problem into an optimization one is proposed, and numerical results are performed for a rectangular domain.

Keywords: Laplacian equation; seawater intrusion; identification; identifiability; inverse source problems

MSC 2010: 35R30; 35B25; 35B35; 35J05; 35J08; 65M32

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About the article

Received: 2018-10-08

Accepted: 2019-03-14

Published Online: 2019-04-17

Published in Print: 2019-08-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 559–574, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2018-0095.

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