Direct algorithms for solving some inverse source problems in 2D elliptic equations

This paper deals with the resolution of some inverse source problems in the 2D elliptic equation from Cauchy data. Two types of sources are considered, pointwise sources and sources having compact support within a finite number of small subdomains. An identification direct algorithm, based on an alg...

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Bibliographic Details
Published in:Inverse problems 2015-10, Vol.31 (10), p.105002-105027
Main Authors: Abdelaziz, Batoul, Badia, Abdellatif El, Hajj, Ahmad El
Format: Article
Language:English
Subjects:
2D Helmholtz's equation
Algebra
algebraic algorithm
Algorithms
Inverse
Inverse problems
inverse source problems
Mathematical analysis
Mathematics
Two dimensional
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Summary:This paper deals with the resolution of some inverse source problems in the 2D elliptic equation from Cauchy data. Two types of sources are considered, pointwise sources and sources having compact support within a finite number of small subdomains. An identification direct algorithm, based on an algebraic approach, is proposed. This is a new result, as far as we know, except in the case which is already considered in El Badia and Ha-Duong (2000 Inverse Problems 16 651-63).
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/31/10/105002