Nonlocal impedance conditions in direct and inverse obstacle scattering

Inverse Problems

Volumn 35, Issue 2, 2019, Pages

  Kress, R ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

generalized impedance condition; inverse scattering; transmission eigenvalues

Indexed keywords

BOUNDARY INTEGRAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR EQUATIONS; REFRACTIVE INDEX;

IMPEDANCE CONDITIONS; INVERSE SCATTERING; NONLINEAR INTEGRAL EQUATIONS; NUMERICAL COMPUTATIONS; TRADITIONAL BOUNDARIES; TRANSMISSION CONDITIONS; TRANSMISSION EIGENVALUES; TRANSMISSION PROBLEM;

INVERSE PROBLEMS;

EID: 85062501159     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/1361-6420/aaf14e     Document Type: Article

References (26)

1. Altundag A and Kress R 2012 An iterative method for a two-dimensional inverse scattering problem for a dielectric J. Inverse Ill-Posed Problem 20 575-90
2. Beyn W-J 2012 An integral method for solving nonlinear eigenvalue problems Linear Algebra Appl. 436 3839-63
3. Cakoni F, Hsiao G C and Wendland W L 2005 On the boundary integral equations method for a mixed boundary value problem of the biharmonic equation Complex Var. Theory Appl. 50 681-96
4. Cakoni F, Ivanyshyn O, Kress R and Le Louër F 2018 A boundary integral equation for the transmission eigenvalue problem for Maxwell's equation Math. Methods Appl. Math. 41 1316-30
5. Cakoni F and Kress R 2017 A boundary integral equation method for the transmission eigenvalue problem Appl. Anal. 96 23-38
6. Colton D, Kirsch A and Päivärinta L 1989 Far field patterns for acoustic waves in an inhomogeneous medium SIAM J. Math. Anal. 20 1472-83
7. Colton D and Kress R 2013 Integral Equation Methods in Scattering Theory (Classics in Applied Mathematics vol 72) (Philadelphia, PA: SIAM)
8. Colton D and Kress R 2013 Inverse Acoustic and Electromagnetic Scattering Theory 3rd edn (New York: Springer)
9. Cossonnière A and Haddar H 2013 Surface integral formulation of the interior transmission problem J. Integral Equ. Appl. 25 341-76
10. Ivanyshyn O, Kress R and Serranho P 2010 Huygens' principle and iterative methods in inverse obstacle scattering Adv. Comput. Math. 33 413-29
11. Kirsch A 1986 The denseness of the far field patterns for the transmission problem IMA J. Appl. Math. 37 213-25
12. Kirsch A 1989 Surface gradient and continuity properties of some integral operators in classical scattering theory Math. Methods Appl. Sci. 11 789-804
13. Kirsch A and Lechleiter A 2013 The inside-outside duality for scattering problems by inhomogeneous media Inverse Problems 29 104011
14. Kleefeld A 2013 A numerical method to compute interior transmission eigenvalues Inverse Problems 29 104012
15. Kleinman R and Martin P 1988 On single integral equations for the transmission problem of acoustics SIAM J. Appl. Math. 48 307-25
16. Kress R and Roach G 1978 Transmission problems for the Helmholtz equation J. Math. Phys. 19 1433-7
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
18. Kress R and Rundell W 2015 A nonlinear integral equation and an iterative algorithm for an inverse source problem J. Integral Equ. Appl. 26 179-98
19. Kress R and Rundell W 2018 Inverse scattering for shape and impedance revisited J. Integral Equ. Appl. 30 293-311
20. McLean W 2000 Strongly Elliptic Systems and Boundary Integral Equations (Cambridge: Cambridge University Press)
21. Lechleiter A and Peters S 2015 The inside-outside duality for inverse scattering problems with near field data Inverse Problems 31 085004
22. Lechleiter A and Rennoch M 2015 Inside-outside duality and the determination of electromagnetic interior transmission eigenvalues SIAM J. Math. Anal. 47 684-705
23. Päivärinta L and Sylvester J 2008 Transmission eigenvalues SIAM J. Math. Anal. 40 738-58
24. Panich O I 1965 On the question of the solvability of the exterior boundary-value problems for the wave equation and Maxwell's equations Usp. Mat. Nauk 20A 221-6 (in Russian)
25. Rynne B P and Sleeman B D 1991 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755-62
26. Taylor M E 1996 Partial Differential Equations (New York: Springer)