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.

参考文献

[1] Carrera J. State of the art of the inverse problem applied to the flow and solute transport problems//Groundwater Flow Quality Modelling, NATO ASI Ser, Ser C. Norwell, Mass:Kluwer Acad, 1998:549-589
[2] Ginn T R, Gushman J H. Inverse methods for subsurface flow:A critical review of stochastic techniques. Stochastic Hydrol Hydraul, 1990, 4:1-26
[3] Kuiper L. A comparaison of several methodsfor inverse for the solution of the inverse problem in the two-dimensional steady state groundwater modeling. Water Resours Res, 1986, 22(5):705-714
[4] McLaughlin D, Towenley L R. A reassessement of the groundwater inverse problem. Water Resour Res, 1996, 32(5):1131-1161
[5] Sun N-Z. Inverse Problems in Groundwater Modelling. Dordrecht, Netherland:Kluwer Academic Publishers, 1994
[6] Yeh W W G. Review of parameter identification procedures in groundwater hydrology:The inverse problem. Water Resources Review, 1986, 2:95-108
[7] Sun N-Z, Yeh W G. Coupled inverse problems in groundwater modelling 1. Sensivity analysis and parameter identification. Water Resources Research, 1990, 26:2507-2525
[8] Tber M H, Talibi M E, Ouaraza D. Parameters identification in a seawater intrusion model using adjoint sensitive method. Math Comput Simul, 2008, 77:301-312
[9] Tber M H, Talibi M E, Ouaraza D. Identification of the hydraulic conductivities in a saltwater intrusion problem. J Inv Ill-Posed Problems, 2007, 15:1-20
[10] Ranjan P, Kazama S, Sawamoto M. Modeling of the dynamics of saltwater-freshwater interface in coastal aquifers//Proceedings of the Joint AOGS Annual Meeting and APHW Second Conference. Singapore, 2004:373-380
[11] Bear J. Dynamics of Fluids in Porous Media. Elsevier, 1972
[12] Bear J, Cheng A H D, Sorek S, Ouazar D, Herrera I. Seawater Intrusion in Coastal Aquifers:Concepts, Methods and Practices. Kluwer Academic Pub, 1999
[13] Bear J, Verruijt A. Modeling Groundwater Flow and Pollution, D. Dordecht, Holland:Reidel Publishing Company, 1987
[14] Choquet C, Diédhiou M M, Rosier C. Derivation of a sharp-diffuse interfaces model for seawater intrusion in a free aquifer. numerical simulations. SIAM J Appl Math, 2016, 76(1):138-158
[15] Alfaro M, Alifrangis P. Convergence of a mass conserving Allen-Cahn equation whose Lagrange multiplier is nonlocal and local. Interfaces Free Bound, to appear
[16] Alfaro M, Hilhorst D, Hiroshi M. Optimal interface width for the Allen-Cahn equation. RIMS Kokyuroku, 2005, 1416:148-160
[17] Cahn J W, Hilliard J E. Free energy of non-uniform systems. I. Interfacial free energy. J Chem Phys, 1958, 28:258-267
[18] Meyers N G. An L_p-estimate for the gradient of solution of second order elliptic divergence equations. Ann Sc Norm Sup Pisa, 1963, 17:189-206
[19] Bensoussan A, Lion J L, Papanicoulou G. Asymptotic Analysis for Periodic Structure. Amsterdam:NorthHolland, 1978
[20] Choquet C, Li J, Rosier C. Uniqueness for cross-diffusion systems issuing from saltwater intrusion problems. Ele J Diff Equ, 2017, 2017(256):1-22
[21] Evans L C. Partial Differential Equations. Graduate Studies in Mathematics, Vol 19. American Mathematical Society, 1998
[22] Lions J L, Magenes E. Problèmes aux limites non homogènes, Vol 1. Dunod, 1968

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

PARAMETERS IDENTIFICATION IN A SALTWATER INTRUSION PROBLEM

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

Metrics

本文评价

推荐阅读 0

[1]	Youssef AHMIDA, Ahmed YOUSSFI. VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES[J]. 数学物理学报(英文版), 2025, 45(5): 2060-2087.
[2]	Anurag JAYSWAL, Vivek SINGH. THE CHARACTERIZATION OF EFFICIENCY AND SADDLE POINT CRITERIA FOR MULTIOBJECTIVE OPTIMIZATION PROBLEM WITH VANISHING CONSTRAINTS[J]. 数学物理学报(英文版), 2019, 39(2): 382-394.
[3]	Elhoussine AZROUL, Badr LAHMI, Ahmed YOUSSFI. STRONGLY NONLINEAR VARIATIONAL PARABOLIC EQUATIONS WITH p(x)-GROWTH[J]. 数学物理学报(英文版), 2016, 36(5): 1383-1404.
[4]	韩军强, 王永达, 钮鹏程. EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE[J]. 数学物理学报(英文版), 2012, 32(5): 1901-1918.
[5]	丁协平. NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS[J]. 数学物理学报(英文版), 2011, 31(3): 1142-1154.
[6]	E. A. Youness; Tarek Emam. CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR MULTI-OBJECTIVE OPTIMIZATION PROBLEMS INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY[J]. 数学物理学报(英文版), 2008, 28(1): 7-16.