S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Communications on Pure and Applied Mathematics, vol.29, issue.4, pp.623-727, 1959.
DOI : 10.1002/cpa.3160120405

D. G. Albert, L. Liu, and M. L. Moran, Time reversal processing for source location in an urban environment, The Journal of the Acoustical Society of America, vol.118, issue.2, pp.616-619, 2005.
DOI : 10.1121/1.1925849

J. P. Aubin, Analyse fonctionnelle appliquée (Tome 2), 1987.

G. Bal and L. Ryzhik, Time Reversal and Refocusing in Random Media, SIAM Journal on Applied Mathematics, vol.63, issue.5, pp.1475-1498, 2004.
DOI : 10.1137/S0036139902401082

M. Balabane, Boundary decomposition for Helmholtz and Maxwell equations 1 : disjoint sub-scatterers, Asymptotic Analysis, vol.38, issue.1, pp.1-10, 2004.

C. B. Amar, N. Gmati, C. Hazard, and K. Ramdani, Numerical Simulation of Acoustic Time Reversal Mirrors, SIAM Journal on Applied Mathematics, vol.67, issue.3, pp.777-791, 2007.
DOI : 10.1137/060654542

URL : https://hal.archives-ouvertes.fr/hal-00140349

M. Balabane and V. Tirel, D??composition de domaine pour un calcul hybride de l'??quation de helmholtz, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.324, issue.3, pp.281-286, 1997.
DOI : 10.1016/S0764-4442(99)80361-9

C. Bardos and M. Fink, Mathematical fondations of the time reversal mirror, Asymptotic Analysis, vol.29, pp.157-182, 2002.

J. G. Berryman, L. Borcea, G. C. Papanicolaou, and C. Tsogka, Statistically stable ultrasonic imaging in random media, The Journal of the Acoustical Society of America, vol.112, issue.4, pp.1509-1522, 2002.
DOI : 10.1121/1.1502266

P. Blomgren, G. Papanicolaou, and H. Zhao, Super-resolution in time-reversal acoustics, The Journal of the Acoustical Society of America, vol.111, issue.1, pp.230-248, 2002.
DOI : 10.1121/1.1421342

A. S. Bonnet and D. , Phénomènes de propagation d'ondes, 2001.

L. Borcea, G. Papanicolaou, and C. Tsogka, Theory and applications of time reversal and interferometric imaging, Inverse Problems, vol.19, issue.6, pp.139-164, 2003.
DOI : 10.1088/0266-5611/19/6/058

URL : https://hal.archives-ouvertes.fr/hal-00106406

L. Borcea, G. Papanicolaou, and C. Tsogka, Optimal waveform design for array imaging, Inverse Problems, vol.23, issue.5, 2006.
DOI : 10.1088/0266-5611/23/5/011

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.6090

L. Borcea, G. Papanicolaou, C. Tsogka, and J. Berryman, Imaging and time reversal in random media, Inverse Problems, vol.18, issue.5, pp.1247-1279, 2002.
DOI : 10.1088/0266-5611/18/5/303

M. Born and E. Wolf, Principles of Optics, 1970.
DOI : 10.1017/CBO9781139644181

S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, 2002.

H. Brezis, Analyse fonctionnelle, Théorie et application, 1992.

N. Burq, D??croissance de l'??nergie locale de l'??quation des ondes pour le probl??me ext??rieur et absence de r??sonance au voisinage du r??el, Acta Mathematica, vol.180, issue.1, pp.1-29, 1988.
DOI : 10.1007/BF02392877

D. Cassereau and M. Fink, Time-reversal of ultrasonic fields. III. Theory of the closed time-reversal cavity, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.39, issue.5, pp.579-793, 1992.
DOI : 10.1109/58.156176

D. H. Chambers and J. G. Berryman, Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids, Inverse Problems, vol.22, issue.6, pp.2145-2163, 2006.
DOI : 10.1088/0266-5611/22/6/014

M. Cheney, D. Isaacson, and M. Lassas, Optimal Acoustic Measurements, SIAM J. Appl. Math, vol.61, pp.1628-1647, 2001.
DOI : 10.1007/0-306-47948-6_71

E. Cherkaeva and A. C. Tripp, On optimal design of transcient electromagnetic waveforms, pp.438-441, 1997.

P. G. Ciarlet, The finite element method for elliptic problems, Studies in mathematics and its applications, 1978.

R. E. Collin, Field theory of guided waves, 1991.

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 1993.

R. Dautray and J. L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques (Tome I), 1985.

A. Derode, A. Tourin, J. De-rosny, M. Tanter, S. Yon et al., Taking Advantage of Multiple Scattering to Communicate with Time-Reversal Antennas, Physical Review Letters, vol.90, issue.1, pp.14301-14302, 2003.
DOI : 10.1103/PhysRevLett.90.014301

E. Domany and O. Entin-wohlman, Application of multiple scattering theory to subsurface defects, Journal of Applied Physics, vol.56, issue.1, pp.137-142, 1984.
DOI : 10.1063/1.333747

C. Draeger and M. Fink, One-channel time-reversal in chaotic cavities: Theoretical limits, The Journal of the Acoustical Society of America, vol.105, issue.2, pp.611-617, 1999.
DOI : 10.1121/1.426251

C. Draeger and M. Fink, One-Channel Time Reversal of Elastic Waves in a Chaotic 2D-Silicon Cavity, Physical Review Letters, vol.79, issue.3, pp.407-410, 1997.
DOI : 10.1103/PhysRevLett.79.407

A. Dubois, K. Belkebir, and M. Saillard, Localization and characterization of twodimensional targets buried in a cluttered environment, Inverse Problems, vol.20, pp.1-17, 2004.

N. Dunford and J. T. Schwartz, Linear operators Part III Spectral operators, 1963.

M. Fink, Time reversed acoustics, M.Sci. Am, pp.91-97, 1999.

M. Fink and C. Prada, Acoustic time-reversal mirrors, Inverse Problems, vol.17, issue.1, pp.1-38, 2001.
DOI : 10.1088/0266-5611/17/1/201

T. Folegot, C. Prada, and M. Fink, Resolution enhancement and separation of reverberation from target echo with the time reversal operator decomposition, The Journal of the Acoustical Society of America, vol.113, issue.6, pp.3155-3160, 2003.
DOI : 10.1121/1.1571541

J. P. Fouque, J. Garnier, and A. Nachbin, Time reversal for dispersive waves in random media, SIAM J. Appl. Math, vol.64, issue.5, pp.1810-1838, 2004.

J. P. Fouque, J. Garnier, A. Nachbin, and K. Solna, Time-reversal refocusing for point source in randomly layered media, Wave Motion, vol.42, issue.3, pp.238-260, 2005.
DOI : 10.1016/j.wavemoti.2005.03.001

URL : https://hal.archives-ouvertes.fr/hal-00018190

C. F. Gaumond, D. M. Fromm, and J. F. Lingevitch, Demonstration at sea of the decomposition-of-the-time-reversal-operator technique, The Journal of the Acoustical Society of America, vol.119, issue.2, pp.976-990, 2006.
DOI : 10.1121/1.2150152

F. K. Gruber, E. A. Marengo, and A. J. Devaney, Time-reversal imaging with multiple signal classification considering multiple scattering between the targets, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3042-3047, 2004.
DOI : 10.1121/1.1738451

O. S. Haddadin and E. S. Ebbini, Ultrasonic focusing through inhomogeneous media by application of the inverse scattering problem, The Journal of the Acoustical Society of America, vol.104, issue.1, pp.313-325, 1998.
DOI : 10.1121/1.423291

C. Hazard, Analyse modale de la propagation des ondes, Mémoire d'HabilitationàHabilitation`Habilitationà Diriger les Recherches, 2001.

C. Hazard and M. Lenoir, Modélisation et résolution desprobì emes de diffraction, cours Math. Appl. -ENSTA, 2001.

C. Hazard and K. Ramdani, Selective Acoustic Focusing Using Time-Harmonic Reversal Mirrors, SIAM Journal on Applied Mathematics, vol.64, issue.3, pp.1057-1076, 2004.
DOI : 10.1137/S0036139903428732

URL : https://hal.archives-ouvertes.fr/inria-00071694

L. Hormander, The analysis of Linear Partial Differential Operators I, 1983.

S. Hou, K. Solna, and H. Zhao, Imaging of location and geometry for extended targets using the response matrix, Journal of Computational Physics, vol.199, issue.1, 2004.
DOI : 10.1016/j.jcp.2004.02.010

S. Hou, K. Solna, and H. Zhao, A direct imaging algorithm for extended targets, Inverse Problems, vol.22, issue.4, pp.1151-1178, 2006.
DOI : 10.1088/0266-5611/22/4/003

D. Isaacson, Distinguishability of Conductivities by Electric Current Computed Tomography, IEEE Transactions on Medical Imaging, vol.5, issue.2, pp.92-95, 1986.
DOI : 10.1109/TMI.1986.4307752

D. R. Jackson and D. R. Dowling, Phase conjugation in underwater acoustics, The Journal of the Acoustical Society of America, vol.89, issue.1, pp.171-181, 1991.
DOI : 10.1121/1.400496

A. Jami and M. Lenoir, A variational formulation for exterior problems in linear hydrodynamics, Comput. Methods Appl. Mech. Engrg, vol.16, pp.341-359, 1978.
URL : https://hal.archives-ouvertes.fr/hal-00974503

B. L. Jonsson, M. Gustafsson, V. H. Weston, M. V. De, and . Hoop, Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal, SIAM Journal on Applied Mathematics, vol.64, issue.6, pp.1954-1986, 2004.
DOI : 10.1137/S0036139903426964

T. Kato, Perturbation Theory for Linear Operators, 1966.

E. Kerbrat, D. Clorennec, C. Prada, D. Royer, D. Cassereau et al., Detection of cracks in a thin air-filled hollow cylinder by application of the DORT method to elastic components of the echo, Ultrasonics, vol.40, issue.1-8, pp.715-720, 2002.
DOI : 10.1016/S0041-624X(02)00199-3

P. Lax and R. Phillips, Scattering Theory, 1989.

J. F. Lingevitch, H. C. Song, and W. A. Kuperman, Time reversed reverberation focusing in a waveguide, J. Acoustic. Soc. Am, vol.111, issue.6, 2002.

P. A. Martin, Multiple Scattering : Interaction of Time-Harmonic Waves with N Obstacles, 2006.
DOI : 10.1017/CBO9780511735110

T. D. Mast, A. I. Nachman, and R. C. Waag, Focusing and imaging using eigenfunctions of the scattering operator, The Journal of the Acoustical Society of America, vol.102, issue.2, pp.715-725, 1997.
DOI : 10.1121/1.419898

G. Micolau, Etude théorique et numérique de la méthode de la Décomposition de l'Opérateur de Retournement Temporel (D.O.R.T) en diffractionélectromagnétiquediffractionélectromagnétique, Thèse de doctorat, 2003.

G. Micolau, M. Saillard, and ". D. , T method as applied to electromagnetic subsurface sensing, Radio Science, vol.38, issue.3, 2003.

G. Micolau, M. Saillard, P. Borderies, and ". D. , DORT method as applied to ultrawideband signals for detection of buried objects, IEEE Transactions on Geoscience and Remote Sensing, vol.41, issue.8, 2003.
DOI : 10.1109/TGRS.2003.814139

N. Mordant, C. Prada, and M. Fink, Highly resolved detection and selective focusing in a waveguide using the D.O.R.T. method, The Journal of the Acoustical Society of America, vol.105, issue.5, pp.2634-2642, 1999.
DOI : 10.1121/1.426879

P. M. Morse and K. U. Ingard, Theoretical Acoustics, 1986.

J. Necàs, Les méthodes directes en théorie deséquationsdeséquations elliptiques, 1967.

J. C. Nédélec, Approximation deséquationsdeséquations intégrales en mécanique et en physique, Ecole polytechnique, 1977.

R. G. Newton, Inverse Schrodinger Scattering in Three Dimensions, 1989.
DOI : 10.1007/978-3-642-83671-8

A. D. Pierce, Acoustics, an introduction to its physical principle and applications, 1981.

C. Prada, Detection and Imaging in Complex Media with the D.O.R.T. Method, Imaging of Complex Media with Acousic and Seismic Waves, pp.107-133, 2002.
DOI : 10.1007/3-540-44680-X_5

C. Prada and M. Fink, Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media, Wave Motion, vol.20, issue.2, pp.151-163, 1994.
DOI : 10.1016/0165-2125(94)90039-6

C. Prada and M. Fink, Separation of interfering acoustic scattered signals using the invariants of the time-reversal operator. Application to Lamb waves characterization, The Journal of the Acoustical Society of America, vol.104, issue.2, pp.801-807, 1998.
DOI : 10.1121/1.423354

C. Prada, E. Kerbrat, D. Cassereau, and M. Fink, Time reversal techniques in ultrasonic nondestructive testing of scattering media, Inverse Problems, vol.18, issue.6, pp.1761-1773, 2002.
DOI : 10.1088/0266-5611/18/6/320

C. Prada, N. Lartillot, and M. Fink, Selective focusing in multiple-target media: the transfer matrix method, Proceedings of IEEE Ultrasonics Symposium, pp.1139-1142, 1993.
DOI : 10.1109/ULTSYM.1993.339588

C. Prada, S. Maneville, D. Spoliansky, and M. Fink, Decomposition of the time reversal operator: Detection and selective focusing on two scatterers, The Journal of the Acoustical Society of America, vol.99, issue.4, pp.2067-2076, 1996.
DOI : 10.1121/1.415393

B. Pinçon and K. Ramdani, Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors

J. Razafiarivelo, Optimisation de la forme de transition entre guidesélectromagnétiquesguidesélectromagnétiques par une méthode intégrale d'´ eléments finis, Thèse de doctorat de l'université Pierre et Marie curie, 1996.

M. Reed and B. Simon, Methods of Modern Mathematical Physics. III : Scattering Theory, 1979.

J. De-la-gorgue-de-rosny, Milieux réverbérants et réversibilité, Thèse de doctorat de l'université Paris VI, 2000.

H. A. Schenck, Helmholtz integral formulation of the sonar equations, The Journal of the Acoustical Society of America, vol.79, issue.5, pp.1423-1433, 1986.
DOI : 10.1121/1.393670

G. T. Schuster, A hybrid BIE+Born series modeling scheme: Generalized Born series, The Journal of the Acoustical Society of America, vol.77, issue.3, pp.865-879, 1985.
DOI : 10.1121/1.392055

H. C. Song, W. A. Kuperman, W. S. Hodgkiss, T. Akal, and C. Ferla, Iterative time reversal in the ocean, The Journal of the Acoustical Society of America, vol.105, issue.6, pp.3176-3184, 1999.
DOI : 10.1121/1.424648

M. Tanter, Application du retournement temporeì a l'hyperthermie ultrasonore du cerveau, Thèse de Doctorat de l, 1999.

M. Tanter, J. F. Aubry, J. Gerber, J. Thomas, and M. Fink, Optimal focusing by spatio-temporal inverse filter Part I. Basic principles, J. Acous. Soc. Am, vol.101, pp.37-47, 2001.

M. Tanter, J. Thomas, and M. Fink, Time reversal and the inverse filter, The Journal of the Acoustical Society of America, vol.108, issue.1, pp.223-234, 2000.
DOI : 10.1121/1.429459

URL : https://hal.archives-ouvertes.fr/hal-00113152

J. L. Thomas, F. Wu, and M. Fink, Time Reversal Focusing Applied to Lithotripsy, Ultrasonic Imaging, vol.18, issue.2, pp.106-121, 1996.
DOI : 10.1177/016173469601800202

H. Tortel, G. Micolau, and M. Saillard, Decomposition of the Time Reversal Operator for Electromagnetic Scattering, Journal of Electromagnetic Waves and Applications, vol.41, issue.5, pp.687-719, 1999.
DOI : 10.1163/156939399X01113

URL : https://hal.archives-ouvertes.fr/hal-00082837

B. R. Vainberg, Asymptotic methods in equations of mathematical physics, 1989.

C. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains, 1975.
DOI : 10.1007/BFb0070581

T. Yokoyama, T. , T. Kikuchi, T. Tsuchiya, and T. , Detection and Selective Focusing on Scatterers Using Decomposition of Time Reversal Operator Method in Pekeris Waveguide Model, Japanese Journal of Applied Physics, vol.40, issue.Part 1, No. 5B, pp.3822-3828, 2001.
DOI : 10.1143/JJAP.40.3822

M. E. Yavus and F. L. Teixeira, Selective focusing via time reversal : time-domain DORT method, 2005.

M. E. Yavus and F. L. Teixeira, Time-domain DORT method for ultrawideband electromagnetic fields under dispersive and conductive random media, 2006 IEEE Antennas and Propagation Society International Symposium, pp.711-714, 2006.
DOI : 10.1109/APS.2006.1710624

H. Zhao, Analysis of the Response Matrix for an Extended Target, SIAM Journal on Applied Mathematics, vol.64, issue.3, pp.725-745, 2004.
DOI : 10.1137/S0036139902415282

N. Zrelli, Etude numérique de quelques solveurs itératifs deprobì emes de propagation d'ondes acoustiques en domaine non borné, Thèse de Doctorat de l'E.N.I.T, 2006.