Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

Inverse Problems

Volumn 31, Issue 4, 2015, Pages

  Bonnet Ben Dhia, Anne Sophie ^a   Chesnel, Lucas ^b   Nazarov, Sergei A ^c,d,e  

^a Centre National de la Recherche Scientifique   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^d PETER THE GREAT ST PETERSBURG POLYTECHNIC UNIVERSITY   (Russian Federation)

^e INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

Author keywords

Asymptotic analysis; Energy identities; Interior transmission problem; Invisibility; Non scattering wavenumbers; Relative scattering matrix

Indexed keywords

ALGORITHMS; ASYMPTOTIC ANALYSIS; SCATTERING PARAMETERS; SET THEORY;

ENERGY IDENTITIES; INTERIOR TRANSMISSION PROBLEMS; INVISIBILITY; RELATIVE SCATTERING; WAVE NUMBERS;

ACOUSTIC WAVE SCATTERING;

EID: 84927649915     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/31/4/045006     Document Type: Article

References (44)

1. Blåsten E, Päivärinta L and Sylvester J 2014 Corners always scatter Commun. Math. Phys. 331 725-53
2. Bonnet-Ben Dhia A-S and Chesnel L 2013 Strongly oscillating singularities for the interior transmission eigenvalue problem Inverse Problems 29 104004
3. Bonnet-Ben Dhia A-S, Chesnel L and Haddar H 2011 On the use of T-coercivity to study the Interior Transmission Eigenvalue Problem C. R. Acad. Sci., Ser. I 340 647-51
4. Bonnet-Ben Dhia A-S and Nazarov S A 2013 Obstacles in acoustic waveguides becoming 'invisible' at given frequencies Acoust. Phys. 59 633-9
5. Bonnet-Ben Dhia A-S, Nazarov S A and Taskinen J 2014 Underwater topography 'invisible' for surface waves at given frequencies Preprint hal-01114632
6. Bukhgeim A L 2008 Recovering a potential from Cauchy data in the two-dimensional case J. Inverse Ill-Posed Probl. 16 19-33
7. Cakoni F 2007 Recent developments in the qualitative approach to inverse electromagnetic scattering theory J. Comput. Appl. Math. 204 242-55
8. Cakoni F and Colton D 2006 Qualitative methods in inverse scattering theory. An introduction Interaction of Mechanics and Mathematics (Berlin: Springer)
9. Cakoni F, Gintides D and Haddar H 2010 The existence of an infinite discrete set of transmission eigenvalues SIAM J. Math. Anal. 42 237-55
10. Cakoni F and Haddar H 2013 Transmission eigenvalues in inverse scattering theory inverse problems and applications Inside Out 60 529-80
11. Cardone G, Durante T and Nazarov S A 2010 The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends SIAM J. Math. Anal. 42 2581-609
12. Cardone G, Nazarov S A and Ruotsalainen K 2012 Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide Sb. Math. 203 153
13. Collino F, M'Barek F and Haddar H 2003 Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems Inverse Problems 19 1279-98
14. Colton D, Haddar H and Piana M 2003 The linear sampling method in inverse electromagnetic scattering theory Inverse Problems 19 105-37
15. Colton D and Kirsch A 1996 A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383
16. Colton D and Kress R 2013 Inverse acoustic and electromagnetic scattering theory 3rd edn (Berlin: Springer) (Applied Mathematical Sciences vol 93)
17. Colton D and Monk P 1988 The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium Q. J. Mech. Appl. Math. 41 97-125
18. Colton D and Monk P 2006 Target identification of coated objects IEEE Trans. Antennas Propag. 54 1232-42
19. Colton D, Piana M and Potthast R 1997 A simple method using morozov's discrepancy principle for solving inverse scattering problems Inverse Problems 13 1477
20. Elschner J and Hu G 2015 Corners and edges always scatter Inverse Problems 31 015003
21. Hille E and Phillips R S 1957 Functional analysis and semi-groups Am. Math. Soc. 808 vol 31 pp
22. Imanuvilov O Yu and Yamamoto M 2012 Inverse boundary value problem for Schrödinger equation in two dimensions SIAM J. Math. Anal. 44 1333-9
23. Kato T 1966 Perturbation Theory for Linear Operators (Berlin: Springer)
24. Kirsch A 1986 The denseness of the far field patterns for the transmission problem IMA J. Appl. Math. 37 213-25
25. Kirsch A and Grinberg N 2008 The Factorization Method for Inverse Problems (Oxford Lecture Series in Mathematics and its Applications) (Oxford: Oxford University Press) 201 vol 36 pp
26. Lakshtanov E and Vainberg B 2012 Ellipticity in the interior transmission problem in anisotropic media SIAM J. Math. Anal. 44 1165-74
27. Lakshtanov E and Vainberg B 2013 Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem Inverse Problems 29 104003
28. Lechleiter A 2009 The factorization method is independent of transmission eigenvalues Inverse Problems Imaging 3 123-38
29. Maz'ya V G, Nazarov S A and Plamenevsk B A 2000 Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains vol 1, 2 (Basel: Birkhäuser) (Translated from the original German 1991 edition)
30. McLean W 2000 Strongly Elliptic Systems and Boundary Integral Equations (Cambridge: Cambridge University Press)
31. Melrose R 1995 Geometric Scattering Theory (Cambridge: Cambridge University Press)
32. Nachman A 1988 Reconstructions from boundary measurements Ann. Math. 128 531-76
33. Nazarov S A 2011 Asymptotic expansions of eigenvalues in the continuous spectrum of a regularly perturbed quantum waveguide Theor. Math. Phys. 167 606-27
34. Nazarov S A 2011 Eigenvalues of the laplace operator with the Neumann conditions at regular perturbed walls of a waveguide J. Math. Sci. 172 555-88
35. Nazarov S A 2011 Trapped waves in a cranked waveguide with hard walls Acoust. Phys. 57 764-71
36. Nazarov S A 2012 Enforced stability of an eigenvalue in the continuous spectrum of a waveguide with an obstacle Comput. Math. and Math. Phys. 52 448-64
37. Nazarov S A 2013 Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide Funct. Anal. Appl. 47 195-209
38. Päivärinta L, Salo M and Vesalainen E V 2014 Strictly convex corners scatter arXiv: 1404.2513
39. Päivärinta L and Sylvester J 2008 Transmission eigenvalues SIAM J. Math. Anal. 40 738-53
40. Potthast R 2006 A survey on sampling and probe methods for inverse problems Inverse Problems 22 R1
41. Robbiano L 2013 Spectral analysis of the interior transmission eigenvalue problem Inverse Problems 29 104001
42. Rynne B P and Sleeman B D 1991 The interior transmission problem and inverse scattering from inhomogeneous media SIAM J. Math. Anal. 22 1755
43. Sylvester J 2012 Discreteness of transmission eigenvalues via upper triangular compact operators SIAM J. Math. Anal. 44 341-54
44. Sylvester J and Uhlmann G 1987 A global uniqueness theorem for an inverse boundary value problem Ann. Math. 125 153-69