Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition

Inverse Problems

Volumn 29, Issue 1, 2013, Pages

  Cakoni, Fioralba ^a   Kress, Rainer ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONDUCTING MEDIUM; GENERALIZED IMPEDANCE BOUNDARY CONDITIONS; IMPEDANCE FUNCTIONS; INTEGRAL EQUATION METHODS; INVERSE BOUNDARY VALUE PROBLEM; NUMERICAL EXAMPLE; OBSTACLE PROBLEMS; RECONSTRUCTION ALGORITHMS; SOLUTION METHODS; UNKNOWN BOUNDARY;

BOUNDARY CONDITIONS; BOUNDARY INTEGRAL EQUATIONS; BOUNDARY VALUE PROBLEMS; LAPLACE EQUATION;

INVERSE PROBLEMS;

EID: 84871754141     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/29/1/015005     Document Type: Article

References (19)

1. Bacchelli V 2009 Uniqueness for the determination of unknown boundary and impedance with the homogeneous Robin condition Inverse Problems 25 015004
2. Bourgeois L and Haddar H 2010 Identification of generalized impedance boundary conditions in inverse scattering problems Inverse Problems Imaging 4 19-38
3. Bourgeois L, Chaulet N and Haddar H 2011 Stable reconstruction of generalized impedance boundary conditions Inverse Problems 27 095002
4. Bourgeois L, Chaulet N and Haddar H 2012 On simultaneous identification of a scatterer and its generalized impedance boundary condition SIAM J. Sci. Comput. 34 A1824-48
5. Cakoni F and Kress R 2007 Integral equations for inverse problems in corrosion detection from partial Cauchy data Inverse Problems Imaging 1 229-45
6. Cakoni F, Kress R and Schuft C 2010 Integral equations for shape and impedance reconstruction in corrosion detection Inverse Problems 26 095012
7. Cakoni F, Kress R and Schuft C 2010 Simultaneous reconstruction of shape and impedance in corrosion detection Methods Appl. Anal. 17 357-78
8. Colton D and Kress R 2013 Inverse Acoustic and Electromagnetic Scattering Theory 3rd edn (New York: Springer)
9. Evans L 1998 Partial Differential Equations (Providence, RI: American Mathematical Society)
10. Haddar H and Kress R 2006 Conformal mapping and an inverse impedance boundary value problem J. Inverse Ill-Posed Problems 14 785-804 (Pubitemid 44678801)
11. Ivanyshyn O and Kress R 2006 Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks J. Integral Eqns Appl. 18 13-38
12. Ivanyshyn O and Kress R 2006 Nonlinear integral equations in inverse obstacle scattering Mathematical Methods in Scattering Theory and Biomedical Engineering ed D I Fotiatis and C V Massalas (Hackensack, NJ: World Scientific) pp 39-50
13. Johansson T and Sleeman B 2007 Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern IMA J. Appl. Math. 72 96-112 (Pubitemid 46189825)
14. Kirsch A 2011 An Introduction to the Mathematical Theory of Inverse Problems 2nd edn (New York: Springer)
15. Kress R 1995 On the numerical solution of a hypersingular integral equation in scattering theory J. Comput. Appl. Math. 61 345-60
16. Kress R 1999 Linear Integral Equations 2nd edn (New York: Springer)
17. Kress R and Rundell W 2005 Nonlinear integral equations and the iterative solution for an inverse boundary value problem Inverse Problems 21 1207-23 (Pubitemid 41090536)
18. McLean W 2000 Strongly Elliptic Systems and Boundary Integral Equations (Cambridge: Cambridge University Press)
19. Pagani C D and Pierotti D 2009 Identifiability problems of defects with the Robin condition Inverse Problems 25 055007