Recovery of the support of a source term in an elliptic differential equation
- 1 August 1997
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 13 (4) , 959-976
- https://doi.org/10.1088/0266-5611/13/4/005
Abstract
The recovery of a source term by exterior measurements is a challenging problem that arises in several applications. In this paper this nonlinear and ill-posed problem is investigated in the case where the source term is assumed to be known but its support is not. Global uniqueness results are presented as well as iterative numerical methods. The numerical approach is based on representing the derivative of the corresponding operator with respect to the boundary of the support.Keywords
This publication has 9 references indexed in Scilit:
- Iterative methods for the reconstruction of an inverse potential problemInverse Problems, 1996
- A convergence analysis of a method of steepest descent and a two–step algorothm for nonlinear ill–posed problemsNumerical Functional Analysis and Optimization, 1996
- Global Uniqueness for a Two-Dimensional Inverse Boundary Value ProblemAnnals of Mathematics, 1996
- The Fisher-Hartwig conjecture and Toeplitz eigenvaluesLinear Algebra and its Applications, 1994
- The prolate matrixLinear Algebra and its Applications, 1993
- Inverse Problems for Metal Oxide Semiconductor Field-Effect Transistor Contact ResistivitySIAM Journal on Applied Mathematics, 1992
- Reconstruction techniques for classical inverse Sturm-Liouville problemsMathematics of Computation, 1992
- Incomplete data problems in x-ray computerized tomographyNumerische Mathematik, 1986
- Some comments on Fourier analysis, uncertainty and modelingSIAM Review, 1983