An inverse problem for Maxwell's equations in isotropic and non-stationary media

References

• Kong , JA . 1990 . Electromagnetic Wave Theory , New York : Wiley .
   Google Scholar
• O'dell , TH . 1970 . “ The Electrodynamics of Magneto-electric Media ” . In Series of Monographs on Selected Topics in Solid State Physics , Edited by: Wohlfarth , EP . 1653 – 1669 . Amsterdam : North-Holland .
   Google Scholar
• Adams , RA . 1975 . Sobolev Spaces , New York : Academic Press .
   Google Scholar
• Li , S . 2005 . An inverse problem for Maxwell's equations in bi-isotropic media . SIAM J. Math. Anal. , 37 : 1027 – 1043 .
   Web of Science ®Google Scholar
• Li , S and Yamamoto , M . 2005 . Inverse source problem for Maxwell's equations in anisotropic media . Appl. Anal. , 84 : 1051 – 1067 .
   Google Scholar
• Li , S and Yamamoto , M . 2007 . An inverse problem for Maxwell's equations in anisotropic media in two dimensions . Chin. Ann. Math. Ser. B. , 28B : 35 – 54 .
   Web of Science ®Google Scholar
• Romanov , VG and Kabanikhin , SI . 1994 . Inverse Problems for Maxwell's Equations , Utrecht : VSP .
   Google Scholar
• Yamamoto , M . 1997 . A mathematical aspect of inverse problems for non-stationary Maxwell's equations . Int. J. Appl. Electromagn. Mech. , 8 : 77 – 98 .
   Web of Science ®Google Scholar
• Yamamoto , M . 1998 . On an inverse problem of determining source terms in Maxwell's equations with a single measurement . Inv. Probl. Tomogr. Image Process. , 15 : 241 – 256 .
   Google Scholar
• Sun , Z and Uhlmann , G . 1992 . An inverse boundary problem for Maxwell's equations . Arch. Ration. Mech. Anal. , 119 : 71 – 93 .
   Web of Science ®Google Scholar
• Bukhgeim , AL and Klibanov , MV . 1981 . Global uniqueness of a class of multidimensional inverse problems . Sov. Math. Dokl. , 24 : 244 – 247 .
   Google Scholar
• Bukhgeim , AL . 2000 . Introduction to the Theory of Inverse Problems , Utrecht : VSP .
   Google Scholar
• Klibanov , MV . 1992 . Inverse problems and Carleman estimates . Inv. Probl. , 8 : 575 – 596 .
   Web of Science ®Google Scholar
• Klibanov , MV and Timonov , A . 2004 . Carleman Estimates for Coefficient Inverse Problems and Numerical Applications , Utrecht : VSP .
   Google Scholar
• Imanuvilov , OY , Isakov , V and Yamamoto , M . 2003 . An inverse problem for the dynamical Lamé system with two sets of boundary data . Commun. Pure Appl. Math. , 56 : 1366 – 1382 .
   Web of Science ®Google Scholar
• Imanuvilov , OY and Yamamoto , M . 2001 . Global Lipschitz stability in an inverse hyperbolic problem by interior observations . Inv. Probl. , 17 : 717 – 728 .
   Web of Science ®Google Scholar
• Imanuvilov , OY and Yamamoto , M . 2003 . Determination of a coefficient in an acoustic equation with a single measurement . Inv. Probl. , 19 : 157 – 171 .
   Web of Science ®Google Scholar
• Isakov , V . 1989 . Uniqueness of the continuation across a time-like hyperplane and related inverse problems for hyperbolic equations . Commun. Partial Differ. Eqns , 14 : 465 – 478 .
   Web of Science ®Google Scholar
• Isakov , V . 2006 . Inverse Problems for Partial Differential Equations , Berlin : Springer-Verlag .
   Google Scholar
• Isakov , V . 2004 . “ Carleman type estimates and their applications ” . In New Analytic and Geometric Methods in Inverse Problems , Edited by: Bingham , K , Kurylev , Y and Somersalo , E . 93 – 125 . Berlin : Springer-Verlag .
   Google Scholar
• Khaĭdarov , A . 1987 . Carleman estimates and inverse problems for second-order hyperbolic equations . Math. USSR Sb. , 58 : 267 – 277 .
   Google Scholar
• Yamamoto , M . 1999 . Uniqueness and stability in multidimensional hyperbolic inverse problems . J. Math. Pure. Appl. , 78 : 65 – 98 .
   Web of Science ®Google Scholar
• Imanuvilov , OY . 2002 . On Carleman estimates for hyperbolic equations . Asymptot. Anal. , 32 : 185 – 220 .
   Web of Science ®Google Scholar