PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

doi:10.1007/s10473-020-0522-x

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1563-1584.doi: 10.1007/s10473-020-0522-x

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

李季¹, Carole ROSIER²

1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing Key Laboratory of Social Economy and Applied Statisties, Chongqing 400067, China;
2. Universite du Littoral Côte d'Opale, UR 2597, LMPA, Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, F-62100 Calais, France, CNRS FR 2037, France

收稿日期:2018-01-31 修回日期:2019-10-19 出版日期:2020-10-25 发布日期:2020-11-04
通讯作者: Carole ROSIER E-mail:rosier@univ-littoral.fr
作者简介:Ji LI,E-mail:liji_maths@email.ctbu.edu.cn
基金资助:
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).

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

Ji LI¹, Carole ROSIER²

1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing Key Laboratory of Social Economy and Applied Statisties, Chongqing 400067, China;
2. Universite du Littoral Côte d'Opale, UR 2597, LMPA, Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, F-62100 Calais, France, CNRS FR 2037, France

Received:2018-01-31 Revised:2019-10-19 Online:2020-10-25 Published:2020-11-04
Contact: Carole ROSIER E-mail:rosier@univ-littoral.fr
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: parameters identification, optimization problem, strongly coupled system, nonlinear parabolic equations, seawater intrusion

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.

Key words: parameters identification, optimization problem, strongly coupled system, nonlinear parabolic equations, seawater intrusion

中图分类号:

49J20

李季, Carole ROSIER. PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM[J]. 数学物理学报(英文版), 2020, 40(5): 1563-1584.

Ji LI, Carole ROSIER. PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1563-1584.

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PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

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