The identification of a penetrable obstacle with mixed transmission conditions from far field measurements

References

• Cakoni , F and Colton , D . 2006 . “ Qualitative Methods in Inverse Scattering Theory: An Introduction ” . In (Interaction of Mechanics and Mathematics) , Berlin : Springer .
   Google Scholar
• Cakoni , F and Colton , D . 2003 . A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media . Proc. Edinb. Math. Soc. , 46 : 293 – 314 .
   Web of Science ®Google Scholar
• McLean , W . 2000 . Strongly Elliptic Systems and Boundary Integral Equations , Cambridge : Cambridge University Press .
   Google Scholar
• Colton , D and Kress , R . 1998 . Inverse Acoustic and Electromagnetic Scattering Theory , 2nd , New York : Springer-Verlag .
   Google Scholar
• Cakoni , F and Colton , D . 2003 . Combined far field operators in electromagnetic inverse scattering theory . Math. Methods Appl. Sci. , 26 : 413 – 429 .
   Google Scholar
• Hähner , P . 2000 . On the uniqueness of the shape of a penetrable, anisotropic obstacle . J. Comput. Appl. Math. , 116 : 167 – 180 .
   Web of Science ®Google Scholar
• Cakoni , F , Colton , D and Monk , P . The determination of boundary coefficients from far field measurements, J. Integral Equ. Appl. , (accepted)
   Google Scholar
• Cakoni , F , Colton , D and Monk , P . 2005 . The determination of the surface conductivity of a partially coated dielectric . SIAM. J. Appl. Math. , 65 : 767 – 789 .
   Web of Science ®Google Scholar
• Cakoni , F , Colton , D and Haddar , H . 2002 . The linear sampling method for anisotropic media . J. Comput. Appl. Math. , 146 : 285 – 299 .
   Web of Science ®Google Scholar
• Cheng , J , Liu , JJ and Nakamura , G . 2003 . Recovery of the shape of an obstacle and the boundary impedance from the far-field pattern . J. Maths Kyoto University , 43 ( 1 ) : 165 – 186 .
   Web of Science ®Google Scholar
• Liu , J , Nakamura , G and Sini , M . 2007 . Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder . SIAM. J. Appl. Math. , 67 ( 4 ) : 1124 – 1146 .
   Web of Science ®Google Scholar
• Nakamura , G and Sini , M . 2007 . Obstacle and boundary determination from scattering data . SIAM J. Math. Anal. , 39 ( 3 ) : 819 – 837 .
   Web of Science ®Google Scholar
• Honda , H , Nakamura , G , Potthast , R and Sini , M . 2008 . The no-response approach and its relation to non-iterative methods for the inverse scattering . Ann. Mat. Pura Appl. , 187 ( 1 ) : 7 – 37 .
   Google Scholar
• Ikehata , M . 1998 . Reconstruction of the shape of the inclusion by boundary measurements . Comm. PDE , 23 : 1459 – 1474 .
   Web of Science ®Google Scholar
• Nakamura , G and Sini , M . Asymptotical behaviour of Green's function of the interior transmission problem , RICAM preprint
   Google Scholar
• Nakamura , G , Potthast , R and Sini , M . 2006 . Unification of the probe and singular sources methods for the inverse boundary value problem by the non-response test . Comm. PDE , 31 ( 10 ) : 1505 – 1528 .
   Web of Science ®Google Scholar
• Potthast , R . 2006 . A survey on sampling and probe methods for inverse problems . Inverse Probl. , 22 ( 2 ) : R1 – R47 .
   Web of Science ®Google Scholar
• Colton , D and Kress , R . 2006 . Using fundamental solutions in inverse scattering . Inverse Probl. , 22 ( 3 ) : R49 – R66 .
   Web of Science ®Google Scholar
• Potthast , R . 2001 . “ Point Sources and Multipoles in Inverse Scattering Theory ” . In Research Notes in Mathematics , Vol. 427 , Boca Raton, FI : Chapman-Hall/CRC .
   Google Scholar
• Arens , T . 2004 . Why linear sampling method works. Inverse Probl. , 20 : 163 – 173 .
   Web of Science ®Google Scholar
• Arens , T and Lechleiter , A . 2009 . The linear sampling method revisited, J. Integral Equ. Appl. , 21 : 179 – 202 .
   Web of Science ®Google Scholar
• Monk , P and Süli , E . 1998 . The adaptive computation of far field patterns by a posteriori error estimation of linear functionals . SIAM J. Numer. Anal. , 36 : 251 – 274 .
   Web of Science ®Google Scholar
• Collino , F and Monk , P . 1998 . The perfectly matched Layer in curvilinear coordinates . SIAM J. Sci. Comput. , 19 : 2061 – 2090 .
   Google Scholar
• Colton , D , Piana , M and Potthast , P . 1997 . A simple method using Morozov's discrepancy principle for solving inverse scattering problems . Inverse Probl. , 13 : 1477 – 1493 .
   Web of Science ®Google Scholar