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Volumn 282, Issue 2, 2003, Pages 479-494

Identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements

Author keywords

Electromagnetic coefficients; Geometric control; Inverse problem; Maxwell's equations; Reconstructions; Wave equation

Indexed keywords


EID: 0038793501     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00709-6     Document Type: Article
Times cited : (9)

References (44)
  • 1
    • 0038002655 scopus 로고    scopus 로고
    • Exact boundary controllability of electromagnetic fields in general regions
    • N.U. Ahmed, T. Wan, Exact boundary controllability of electromagnetic fields in general regions, Dynamic Systems Appl. 5 (1996) 229-243.
    • (1996) Dynamic Systems Appl. , vol.5 , pp. 229-243
    • Ahmed, N.U.1    Wan, T.2
  • 2
    • 0036222666 scopus 로고    scopus 로고
    • Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium
    • C. Alves, H. Ammari, Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium, SIAM J. Appl. Math. 62 (2002) 94-106.
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 94-106
    • Alves, C.1    Ammari, H.2
  • 3
    • 0038679242 scopus 로고    scopus 로고
    • An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume
    • H. Ammari, An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume, SIAM J. Control Optim. 41 (2003) 1194-1211.
    • (2003) SIAM J. Control Optim. , vol.41 , pp. 1194-1211
    • Ammari, H.1
  • 4
    • 0008808677 scopus 로고    scopus 로고
    • Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter
    • to appear
    • H. Ammari, S. Moskow, M. Vogelius, Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter, ESAIM, Control Optim. Calc. Var., to appear.
    • ESAIM, Control Optim. Calc. Var.
    • Ammari, H.1    Moskow, S.2    Vogelius, M.3
  • 5
    • 0035596680 scopus 로고    scopus 로고
    • Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell equations
    • H. Ammari, M. Vogelius, D. Volkov, 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 (2001) 769-814.
    • (2001) J. Math. Pures Appl. , vol.80 , pp. 769-814
    • Ammari, H.1    Vogelius, M.2    Volkov, D.3
  • 6
    • 0026923885 scopus 로고
    • Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary
    • C. Bardos, G. Lebeau, J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim. 30 (1992) 1024-1065.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 1024-1065
    • Bardos, C.1    Lebeau, G.2    Rauch, J.3
  • 7
    • 0002994809 scopus 로고
    • Boundary control, wave field continuation and inverse problems for the wave equation
    • M.I. Belishev, Y, Kurylev, Boundary control, wave field continuation and inverse problems for the wave equation, Comput. Math. Appl. 22 (1991) 27-52.
    • (1991) Comput. Math. Appl. , vol.22 , pp. 27-52
    • Belishev, M.I.1    Kurylev, Y.2
  • 8
    • 0034425488 scopus 로고    scopus 로고
    • Boundary control of the Maxwell dynamical system: Lack of controllability by topological reasons
    • M.I. Belishev, A.K. Glasman, Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons, ESAIM, Control Optim. Calc. Var. 5 (2000) 207-217.
    • (2000) ESAIM, Control Optim. Calc. Var. , vol.5 , pp. 207-217
    • Belishev, M.I.1    Glasman, A.K.2
  • 9
    • 0038340667 scopus 로고    scopus 로고
    • On the uniqueness of the reconstruction of the parameters of the Maxwell system from dynamic boundary data
    • M.I. Belishev, V.M. Isakov, On the uniqueness of the reconstruction of the parameters of the Maxwell system from dynamic boundary data, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov 285 (2002).
    • (2002) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov , vol.285
    • Belishev, M.I.1    Isakov, V.M.2
  • 10
    • 0038340666 scopus 로고    scopus 로고
    • A dynamic inverse problem for the Maxwell system: Reconstruction of the velocity in the regular zone (the B-C method)
    • M.I. Belishev, A.K. Glasman, A dynamic inverse problem for the Maxwell system: reconstruction of the velocity in the regular zone (the B-C method), St. Petersburg Math. J. 12 (2001) 279-316.
    • (2001) St. Petersburg Math. J. , vol.12 , pp. 279-316
    • Belishev, M.I.1    Glasman, A.K.2
  • 11
    • 0042247791 scopus 로고    scopus 로고
    • Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfection of small area
    • to appear
    • E. Beretta, A. Mukherjee, M. Vogelius, Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfection of small area, Z. Angew. Math. Phys., to appear.
    • Z. Angew Math. Phys.
    • Beretta, E.1    Mukherjee, A.2    Vogelius, M.3
  • 12
    • 0038340670 scopus 로고    scopus 로고
    • Determination of point wave sources by pointwise observations: Stability and reconstruction
    • G. Bruckner, M. Yamamoto, Determination of point wave sources by pointwise observations: stability and reconstruction, Inverse Problems 16 (2000) 723-748.
    • (2000) Inverse Problems , vol.16 , pp. 723-748
    • Bruckner, G.1    Yamamoto, M.2
  • 13
    • 0002713385 scopus 로고
    • On an Inverse Boundary Value Problem
    • Soc. Brasileíra de Matemática, Rio de Janeiro
    • A.P. Calderón, On an Inverse Boundary Value Problem, in: Semin. Numer. Anal. Appl. Contin. Phys., Soc. Brasileíra de Matemática, Rio de Janeiro, 1980, pp. 65-73.
    • (1980) Semin. Numer. Anal. Appl. Contin. Phys. , pp. 65-73
    • Calderón, A.P.1
  • 14
    • 0000932785 scopus 로고    scopus 로고
    • Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computional reconstruction
    • D.J. Cedio-Fengya, S. Moskow, M. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computional reconstruction, Inverse Problems 14 (1998) 553-595.
    • (1998) Inverse Problems , vol.14 , pp. 553-595
    • Cedio-Fengya, D.J.1    Moskow, S.2    Vogelius, M.3
  • 15
    • 0003228130 scopus 로고    scopus 로고
    • Partial Differential Equations
    • Amer. Math. Society, Providence, RI
    • L.C. Evans, Partial Differential Equations, in: Grad. Stud. in Math., Amer. Math. Society, Providence, RI, 1998.
    • (1998) Grad. Stud. in Math.
    • Evans, L.C.1
  • 16
    • 0007473029 scopus 로고
    • Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
    • A. Friedman, M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence, Arch. Rat. Mech. Anal. 105 (1989) 299-326.
    • (1989) Arch. Rat. Mech. Anal. , vol.105 , pp. 299-326
    • Friedman, A.1    Vogelius, M.2
  • 17
    • 0032122895 scopus 로고    scopus 로고
    • Identifying a spatial body force in linear elastodynamics via traction measurements
    • M. Grasselli, M. Yamamoto, Identifying a spatial body force in linear elastodynamics via traction measurements, SIAM J. Control Optim. 36 (1998) 1190-1206.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 1190-1206
    • Grasselli, M.1    Yamamoto, M.2
  • 18
    • 84973553839 scopus 로고    scopus 로고
    • Inverse Problems for Partial Differential Equations
    • Springer-Verlag, New York
    • V. Isakov, Inverse Problems for Partial Differential Equations, in: Appl. Math. Sci., Vol. 127, Springer-Verlag, New York, 1998.
    • (1998) Appl. Math. Sci. , vol.127
    • Isakov, V.1
  • 19
    • 0038002659 scopus 로고    scopus 로고
    • Total determination of material parameters from electromagnetic boundary information
    • M.S. Joshi, S.R. McDowall, Total determination of material parameters from electromagnetic boundary information, Pacific J. Math. 193 (2000) 107-129.
    • (2000) Pacific J. Math. , vol.193 , pp. 107-129
    • Joshi, M.S.1    McDowall, S.R.2
  • 20
    • 0025399324 scopus 로고
    • Boundary controllability of Maxwell's equations in a spherical region
    • K.A. Kime, Boundary controllability of Maxwell's equations in a spherical region, SIAM J. Control Optim. 28 (1990) 294-319.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 294-319
    • Kime, K.A.1
  • 21
    • 0002641721 scopus 로고
    • Boundary stabilization, observation and control of Maxwell's equations
    • V. Komornik, Boundary stabilization, observation and control of Maxwell's equations, Panamer. Math. J. 4 (1994) 47-61.
    • (1994) Panamer. Math. J. , vol.4 , pp. 47-61
    • Komornik, V.1
  • 22
    • 0024626689 scopus 로고
    • Exact boundary controllability of Maxwell's equations in a general region
    • J.E. Lagnese, Exact boundary controllability of Maxwell's equations in a general region, SIAM J. Control Optim. 27 (1989) 374-388.
    • (1989) SIAM J. Control Optim. , vol.27 , pp. 374-388
    • Lagnese, J.E.1
  • 23
    • 0037664902 scopus 로고
    • Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome 1, Contrôlabilité Exacte, Masson, Paris
    • J.L. Lions, Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome 1, Contrôlabilité Exacte, Masson, Paris, 1988.
    • (1988)
    • Lions, J.L.1
  • 24
    • 0038679236 scopus 로고    scopus 로고
    • Boundary determination material parameters from electromagnetic boundary information
    • S.R. McDowall, Boundary determination material parameters from electromagnetic boundary information, Inverse Problems 13 (1997) 153-163.
    • (1997) Inverse Problems , vol.13 , pp. 153-163
    • McDowall, S.R.1
  • 25
    • 23044520864 scopus 로고    scopus 로고
    • An electromagnetic inverse problem in chiral media
    • S.R. McDowall, An electromagnetic inverse problem in chiral media, Trans. Amer. Math. Soc. 352 (2000) 2993-3013.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 2993-3013
    • McDowall, S.R.1
  • 26
    • 0030550779 scopus 로고    scopus 로고
    • Global uniqueness for a two-dimensional inverse boundary value problem
    • A. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. Math. 143 (1996) 71-96.
    • (1996) Ann. Math. , vol.143 , pp. 71-96
    • Nachman, A.1
  • 27
    • 0001282381 scopus 로고
    • Contrôlabilité exacte sur une partie do bord des équations de Maxwell
    • O. Nalin, Contrôlabilité exacte sur une partie do bord des équations de Maxwell, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989) 811-815.
    • (1989) C. R. Acad. Sci. Paris Sér. I Math. , vol.309 , pp. 811-815
    • Nalin, O.1
  • 28
    • 0033699434 scopus 로고    scopus 로고
    • Exact boundary controllability of Maxwell's equations in heterogeneous media and an application to an inverse source problem
    • S. Nicaise, Exact boundary controllability of Maxwell's equations in heterogeneous media and an application to an inverse source problem, SIAM J. Control Optim. 38 (2000) 1145-1170.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 1145-1170
    • Nicaise, S.1
  • 29
    • 84973999369 scopus 로고
    • An inverse boundary value problem in electrodynamics
    • P. Ola, L. Païvärinta, E. Somersalo, An inverse boundary value problem in electrodynamics, Duke Math. J. 70 (1993) 617-653.
    • (1993) Duke Math. J. , vol.70 , pp. 617-653
    • Ola, P.1    Païvärinta, L.2    Somersalo, E.3
  • 30
    • 0034426084 scopus 로고    scopus 로고
    • Contrôle et stabilisation d'ondes électromagnétiques
    • K.D. Phung, Contrôle et stabilisation d'ondes électromagnétiques, ESAIM, Control Optim. Calc. Var. 5 (2000) 87-137.
    • (2000) ESAIM, Control Optim. Calc. Var. , vol.5 , pp. 87-137
    • Phung, K.D.1
  • 31
    • 0009975697 scopus 로고
    • Applications de la contrôlabilité exacte à quelques problèmes inverses hyperboliques
    • 1320
    • J.P. Puel, M. Yamamoto, Applications de la contrôlabilité exacte à quelques problèmes inverses hyperboliques, C. R. Acad. Sci. Paris Sér 1320 (1995) 1171-1176.
    • (1995) C. R. Acad. Sci. Paris Sér , pp. 1171-1176
    • Puel, J.P.1    Yamamoto, M.2
  • 32
    • 0001476916 scopus 로고    scopus 로고
    • On a global estimate in a linear inverse hyperbolic problem
    • J.P. Puel, M. Yamamoto, On a global estimate in a linear inverse hyperbolic problem, Inverse Problems 12 (1996) 995-1002.
    • (1996) Inverse Problems , vol.12 , pp. 995-1002
    • Puel, J.P.1    Yamamoto, M.2
  • 33
    • 0000571030 scopus 로고    scopus 로고
    • Smoothing property in multidimensional inverse hyperbolic problems: Applications to uniqueness and stability
    • J.P. Puel, M. Yamamoto, Smoothing property in multidimensional inverse hyperbolic problems: applications to uniqueness and stability, J. Inverse Ill-Posed Problems 4 (1996) 283-296.
    • (1996) J. Inverse Ill-Posed Problems , vol.4 , pp. 283-296
    • Puel, J.P.1    Yamamoto, M.2
  • 34
    • 0038002661 scopus 로고    scopus 로고
    • Generic well-posedness in a multidimensional inverse hyperbolic problem
    • J.P. Puel, M. Yamamoto, Generic well-posedness in a multidimensional inverse hyperbolic problem, J. Inverse Ill-Posed Problems 5 (1997) 55-83.
    • (1997) J. Inverse Ill-Posed Problems , vol.5 , pp. 55-83
    • Puel, J.P.1    Yamamoto, M.2
  • 35
    • 0000587767 scopus 로고
    • Uniqueness for an inverse problem for the wave equation
    • Rakesh, W. Symes, Uniqueness for an inverse problem for the wave equation, Comm. Partial Differential Equations 13 (1988) 87-96.
    • (1988) Comm. Partial Differential Equations , vol.13 , pp. 87-96
    • Rakesh, A.1    Symes, W.2
  • 37
    • 0001110912 scopus 로고
    • A global uniqueness theorem for an inverse boundary value problem
    • J. Sylvester, G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. Math. 125 (1987) 153-169.
    • (1987) Ann. Math. , vol.125 , pp. 153-169
    • Sylvester, J.1    Uhlmann, G.2
  • 38
    • 38249007884 scopus 로고
    • A linearized inverse boundary value problem for Maxwell's equations
    • E. Somersalo, D. Isaacson, M. Cheney, A linearized inverse boundary value problem for Maxwell's equations, J. Comput. Appl. Math. 42 (1992) 123-136.
    • (1992) J. Comput. Appl. Math. , vol.42 , pp. 123-136
    • Somersalo, E.1    Isaacson, D.2    Cheney, M.3
  • 39
    • 0025450778 scopus 로고
    • On the continuous dependence for an inverse initial boundary value problem for the wave equation
    • Z. Sun, On the continuous dependence for an inverse initial boundary value problem for the wave equation, J. Math. Anal. Appl. 150 (1990) 188-204.
    • (1990) J. Math. Anal. Appl. , vol.150 , pp. 188-204
    • Sun, Z.1
  • 40
    • 0038679238 scopus 로고
    • Well-posedness of some inverse hyperbolic problems by the Hilbert uniqueness method
    • M. Yamamoto, Well-posedness of some inverse hyperbolic problems by the Hilbert uniqueness method, J. Inverse Ill-Posed Problems 2 (1994) 349-368.
    • (1994) J. Inverse Ill-Posed Problems , vol.2 , pp. 349-368
    • Yamamoto, M.1
  • 41
    • 0001147202 scopus 로고
    • Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method
    • M. Yamamoto, Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method, Inverse Problems 11 (1995) 481-496.
    • (1995) Inverse Problems , vol.11 , pp. 481-496
    • Yamamoto, M.1
  • 42
    • 85015385406 scopus 로고    scopus 로고
    • Determination of forces in vibrations of beams and plates by pointwise and line observations
    • M. Yamamoto, Determination of forces in vibrations of beams and plates by pointwise and line observations, J. Inverse Ill-Posed Problems 4 (1996) 437-457.
    • (1996) J. Inverse Ill-Posed Problems , vol.4 , pp. 437-457
    • Yamamoto, M.1
  • 43
    • 0034398617 scopus 로고    scopus 로고
    • Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities
    • M. Vogelius, D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities, Math. Model. Numer. Anal. 34 (2000) 723-748.
    • (2000) Math. Model. Numer. Anal. , vol.34 , pp. 723-748
    • Vogelius, M.1    Volkov, D.2
  • 44
    • 0037664905 scopus 로고    scopus 로고
    • Exact boundary controllability for a Maxwell problem
    • N. Weck, Exact boundary controllability for a Maxwell problem, SIAM J. Control Optim. 38 (2000) 736-750.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 736-750
    • Weck, N.1


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