PARAMETER IDENTIFICATION BY OPTIMIZATION METHOD FOR A POLLUTION PROBLEM IN POROUS MEDIA

doi:10.1016/S0252-9602(18)30818-X

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (4): 1345-1360.doi: 10.1016/S0252-9602(18)30818-X

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PARAMETER IDENTIFICATION BY OPTIMIZATION METHOD FOR A POLLUTION PROBLEM IN POROUS MEDIA

R. ABOULAICH¹, B. ACHCHAB², A. DAROUICHI³

1. LERMA, Ecole Mohammadia d'Ingénieurs Université de Mohammed V-Agdal, Avenue Ibn Sina B. P 765, Agdal, Rabat, Maroc;
2. Université Hassan 1, Ecde Supérieure de Technologic Berrechi, and LAMSAD, ESTB, B. P 218 Berrechid, Maroc;
3. Université Cadi Ayyad, Ecole Supérieure de Technologie, B. P 383 Essaouira, Maroc

Received:2016-05-26 Revised:2017-10-11 Online:2018-08-25 Published:2018-08-25
Supported by:
This work was supported in part by the CNRST Morocco, the Volkswagen Foundation:Grant number I/79315 and Hydromed project.

Abstract

Abstract:

In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost functional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.

Key words: inverse problem, coefficient identification, optimization method, pollution problem, porous media

R. ABOULAICH, B. ACHCHAB, A. DAROUICHI. PARAMETER IDENTIFICATION BY OPTIMIZATION METHOD FOR A POLLUTION PROBLEM IN POROUS MEDIA[J].Acta mathematica scientia,Series B, 2018, 38(4): 1345-1360.

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PARAMETER IDENTIFICATION BY OPTIMIZATION METHOD FOR A POLLUTION PROBLEM IN POROUS MEDIA

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