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A nonlinear optimization method applied to the hydraulic conductivity identification in unconfined aquifers. (English) Zbl 1425.76051

Summary: This article is concerned with the identification, from observations or field measurements, of the hydraulic conductivity for the saltwater intrusion problem in an unconfined aquifer. The involved model consists in a cross-diffusion system describing the evolutions of two interfaces: one between freshwater and saltwater and the other one between the saturated and unsaturated zones of the aquifer. The inverse problem is formulated as an optimization problem, where the cost function is a least square functional measuring the discrepancy between experimental interfaces depths 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, we establish the first-order necessary optimality conditions. A numerical method is implemented to solve this identification problem. Some numerical results are presented to illustrate the ability of the method to determine the unknown parameters.

MSC:

76B75 Flow control and optimization for incompressible inviscid fluids
90C30 Nonlinear programming
49S05 Variational principles of physics
49J20 Existence theories for optimal control problems involving partial differential equations
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
45M15 Periodic solutions of integral equations
76R99 Diffusion and convection
49N45 Inverse problems in optimal control

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References:

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