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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 5
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Original Articles

Asymptotic behaviour of the energy for electromagnetic systems in the presence of small inhomogeneities

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Pages 857-877 | Received 07 Sep 2009, Accepted 27 Dec 2010, Published online: 22 Feb 2011

References

  • Ammari , H , Iakovleva , E , Lesselier , D and Perrusson , G . 2007 . MUSIC-type electromagnetic imaging of a collection of small three-dimensional inclusions . SIAM Sci. Comput. , 29 : 674 – 709 .
  • Vogelius , M and Volkov , D . 2000 . Asymptoti formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneties . Math. Model. Numer. Anal. , 34 : 723 – 748 .
  • Ammari , H , Vogelius , MS and Volkov , D . 2001 . Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations . J. Math. Pures Appl. , 80 : 769 – 814 .
  • Ammari , H and Khelifi , A . 2003 . Electromagnetic Scattering by Small Dielectric Inhomogeinities . J. Math. Pures Appl. , 82 : 749 – 842 .
  • Daveau , C and Khelifi , A . 2008 . On the perturbation of the electromagnetic energy due to the presence of small inhomogeneities . C. R. Acad. Sci. Paris, Ser. I , 346 : 287 – 292 .
  • Cole , JD . 1968 . Perturbation Methods in Applied Mathematics , Walthan , MA : Blaisdell .
  • Il'in , AM . 1992 . Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, Translations of Mathematical Monographs , Vol. 102 , Providence , RI : American Mathematical Society .
  • Schiffer , M and Szegö , G . 1949 . Virtual mass and polarization . Trans. Amer. Math. Soc. , 67 : 130 – 205 .
  • Cedio-Fengya , DJ , Moskow , S and Vogelius , M . 1998 . Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction . Inverse Probl. , 14 : 553 – 595 .
  • Friedman , A and Vogelius , M . 1989 . Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence . Arch. Rat. Mech. Anal. , 105 : 299 – 326 .
  • Barrett , TW and Grimes , DM . 1995 . Advanced Electromagnetism: Foundations, Theory, & Applications , Singapore : World Scientific .
  • Ziolkowski , RW . 1989 . Localized transmission of electromagnetic energy . Phys. Rev. A , 39 : 2005
  • Campos , I and Jimenez , JL . 1992 . About Poynting's theorem . Eur. J. Phys. , 13 : 117 – 121 .
  • M. Lockwood, C.J. Davis, The correct application of Poynting's theorem to the time-dependent magnetosphere: Reply to Heikkila, Ann. Geophys. 17 (1999), pp. 178–181
  • Morawetz , CS . 1975 . Decay of solutions of the exterior problem for the wave equation . Commun. Pure Appl. Math. , 28 : 229 – 264 .
  • Ralston , J . 1979 . Note on the decay of acoustic waves . Duke Math. J. , 4 I : 799 – 804 .
  • Ducomet , B . 1995 . Decay of electromagnetic energy in a perturbed half-space . Computers Math. Appli. , 29 ( 3 ) : 13 – 21 .
  • Jaime , E , Rivera , M , Naso , MG and Vuk , E . 2004 . Asymptotic behaviour of the energy for electromagnetic systems with memory . Math. Meth. Appl. Sci. , 27 : 819 – 841 .
  • Cazenave , T and Haraux , A . 1990 . Introduction aux problmes dvolutions semi-linaires . SMAI, Math. Appl. ,
  • Hazard , C and Lenoir , M . 1996 . On the solution of time-harmonic scattering problems for Maxwell's equations . SIAM J. Math. Anal. , 27 ( 6 ) : 1597 – 1630 .
  • Pazy , A . 1978 . Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences , Vol. 44 , New York : Springer .
  • Kong , JA . 1986 . Electromagnetic Wave Theory , New York : John Wiley .

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