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Parameters Identification in a Saltwater Intrusion Problem

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Abstract

This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model. Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing Key Laboratory of Social Economy and Applied Statisties, Chongqing, 400067, China

    Ji Li

  2. LMPA, Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, Universite du Littoral Côte d’Opale, UR 2597, F-62100, Calais, France

    Carole Rosier

  3. CNRS FR 2037, Calais, France

    Carole Rosier

Authors
  1. Ji Li
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  2. Carole Rosier
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Correspondence to Carole Rosier.

Additional information

The first author was supported by the Natural Science Foundation of Chongqing Municipal Education Commission (KJ1706167), and the Program for the introduction of High-Level Talents (1756006, 1752003).

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Li, J., Rosier, C. Parameters Identification in a Saltwater Intrusion Problem. Acta Math Sci 40, 1563–1584 (2020). https://doi.org/10.1007/s10473-020-0522-x

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  • DOI: https://doi.org/10.1007/s10473-020-0522-x

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