An Iterative Regularization Method for a Class of Inverse Boundary Value Problems of Elliptic Type

被引：0

作者：

Zouyed, Fairouz ^{[1
]}

Debbouche, Souheyla ^{[2
]}

机构：

[1] Univ Badji Mokhtar Annaba, Appl Math Lab, POB 12, Annaba 23000, Algeria

[2] Univ Larbi Ben Mhidi, Dept Math, Oum El Bouaghi, Algeria

来源：

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY | 2020年 / 16卷 / 01期

关键词：

inverse problems; ill-posed problems; elliptic problems; iterative regularization method; CAUCHY-PROBLEM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the problem of determining an unknown source and an unknown boundary condition u(0) in a boundary value problem of elliptic type from extra measurements at internal points. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. For solving the considered problem an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularization approximation is obtained. Moreover, the numerical results are presented to illustrate the accuracy and efficiency of this method.

引用

页码：66 / 85

页数：20

共 17 条

[1]

Bakushinsky A. B., 2004, MATH APPL, V577

[2]

Bastay G., 1995, LINKOPING STUDIES SC, P392

[3]

Baumeister J., 2001, J INVERSE ILL-POSE P, V9. 1, P1

[4] An alternating iterative procedure for the Cauchy problem for the Helmholtz equation [J].

Berntsson, F. ;

Kozlov, V. A. ;

Mpinganzima, L. ;

Turesson, B. O. .

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2014, 22 (01) :45-62

[5] Two regularization methods for a class of inverse boundary value problems of elliptic type [J].

Bouzitouna, Abdallah ;

Boussetila, Nadjib ;

Rebbani, Faouzia .

BOUNDARY VALUE PROBLEMS, 2013,

[6] A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions [J].

Deuflhard, P ;

Engl, HW ;

Scherzer, O .

INVERSE PROBLEMS, 1998, 14 (05) :1081-1106

[7]

Goldstein J.A., 1985, Semigroups of Linear Operators and Applications

[8] FUNKTIONENTHEORETISCHE BESTIMMUNG DES AUSSENFELDES ZU EINER ZWEIDIMENSIONALEN MAGNETOHYDROSTATISCHEN KONFIGURATION [J].

GORENFLO, R .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1965, 16 (02) :279-&

[9]

Johnson CR, 1997, CRIT REV BIOMED ENG, V25, P1, DOI 10.1615/CritRevBiomedEng.v25.i1.10

[10]

Kozlov V. A., 1990, Leningrad Math. J., V1, P1207

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