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.

中文翻译：

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盐水入侵问题中的参数识别

本文致力于通过观察或现场测量确定承压含水层中盐水入侵问题的水力传导系数 K。所涉及的 PDE 模型是由边界条件和初始条件完成的非线性抛物线-椭圆方程的耦合系统。主要的未知数是咸水/淡水界面深度和淡水水头。逆问题被表述为优化问题，其中成本函数是最小二乘函数，用于测量实验数据与模型提供的数据之间的差异。将精确问题作为优化问题的约束并引入与成本函数相关的拉格朗日函数，我们证明了最优系统至少有一个解。而且，