메뉴 건너뛰기




Volumn 5, Issue 3, 2011, Pages 675-694

Explicit characterization of the support of non-linear inclusions

Author keywords

Impedance tomography; Inverse problems; Inverse scattering; Nonlinear PDE of elliptic type

Indexed keywords


EID: 80051887825     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2011.5.675     Document Type: Article
Times cited : (11)

References (25)
  • 1
    • 35348845804 scopus 로고    scopus 로고
    • High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension
    • G. Baruch, G. Fibich and S. Tsynkov, High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension, J. Comput. Phys., 227 (2007), 820-850.
    • (2007) J. Comput. Phys , vol.227 , pp. 820-850
    • Baruch, G.1    Fibich, G.2    Tsynkov, S.3
  • 2
    • 0035541164 scopus 로고    scopus 로고
    • Explicit characterization of inclusions in electrical impedance tomography
    • M. Brühl, Explicit characterization of inclusions in electrical impedance tomography, SIAM J. Math. Anal., 32 (2001), 1327-1341.
    • (2001) SIAM J. Math. Anal , vol.32 , pp. 1327-1341
    • Brühl, M.1
  • 3
    • 77950574432 scopus 로고    scopus 로고
    • The existence of an infinite discrete set of transmission eigenvalues
    • F. Cakoni, H. Haddar and D. Gintides, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255.
    • (2010) SIAM J. Math. Anal , vol.42 , pp. 237-255
    • Cakoni, F.1    Haddar, H.2    Gintides, D.3
  • 4
    • 0001384370 scopus 로고
    • Determination of the unknown coeffcient k(u) in the equation rk(u)ru = 0 from overspecified boundary data
    • J. R. Cannon, Determination of the unknown coeffcient k(u) in the equation ∇k(u)∇u = 0 from overspecified boundary data, J. Math. Anal. Appl., 18 (1967), 112-114.
    • (1967) J. Math. Anal. Appl , vol.18 , pp. 112-114
    • Cannon, J.R.1
  • 5
    • 0003275409 scopus 로고
    • Inverse Acoustic and Electromagnetic Scattering Theory
    • Springer-Verlag, Berlin
    • D. L. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory, " Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1992.
    • (1992) Applied Mathematical Sciences , vol.93
    • Colton, D.L.1    Kress, R.2
  • 6
    • 0003228130 scopus 로고    scopus 로고
    • Partial Differential Equations
    • American Mathematical Society, Providence, RI
    • L. C. Evans, "Partial Differential Equations, " Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 7
    • 0035452089 scopus 로고    scopus 로고
    • Vectorial and random effects in self-focusing and in multiple filamentation
    • G. Fibich and B. Ilan, Vectorial and random effects in self-focusing and in multiple filamentation, Physica D, 157 (2001), 112-146.
    • (2001) Physica D , vol.157 , pp. 112-146
    • Fibich, G.1    Ilan, B.2
  • 8
    • 0035118917 scopus 로고    scopus 로고
    • Nonlinear current ow in superconductors with restricted geometries
    • M. Friesen and A. Gurevich, Nonlinear current ow in superconductors with restricted geometries, Phys. Rev. B, 63 (2001), 064521.
    • (2001) Phys. Rev. B , vol.63 , pp. 064521
    • Friesen, M.1    Gurevich, A.2
  • 10
    • 0036097959 scopus 로고    scopus 로고
    • The linear sampling method in inverse obstacle scattering for impedance boundary conditions
    • N. Grinberg and A. Kirsch, The linear sampling method in inverse obstacle scattering for impedance boundary conditions, J. Inverse Ill-Posed Probl., 10 (2002), 171-185.
    • (2002) J. Inverse Ill-Posed Probl , vol.10 , pp. 171-185
    • Grinberg, N.1    Kirsch, A.2
  • 12
    • 84990587399 scopus 로고
    • Global uniqueness for a semilinear elliptic inverse problem
    • V. Isakov and J. Sylvester, Global uniqueness for a semilinear elliptic inverse problem, Comm. Pure. Appl. Math., 47 (1994), 1403-1410.
    • (1994) Comm. Pure. Appl. Math , vol.47 , pp. 1403-1410
    • Isakov, V.1    Sylvester, J.2
  • 13
    • 0001311566 scopus 로고
    • Global uniqueness for a two-dimensional semilinear elliptic inverse problem
    • V. Isakov and A. I. Nachman, Global uniqueness for a two-dimensional semilinear elliptic inverse problem, Trans. Amer. Math. Soc., 347 (1995), 3375-3390.
    • (1995) Trans. Amer. Math. Soc , vol.347 , pp. 3375-3390
    • Isakov, V.1    Nachman, A.I.2
  • 14
    • 2942606169 scopus 로고    scopus 로고
    • Inverse problem for a nonlinear Helmholtz equation
    • E. Jalade, Inverse problem for a nonlinear Helmholtz equation, Ann. I. H. Poincaré Anal. Non Linéaire, 21 (2004), 517-531.
    • (2004) Ann. I. H. Poincaré Anal. Non Linéaire , vol.21 , pp. 517-531
    • Jalade, E.1
  • 15
    • 0036685542 scopus 로고    scopus 로고
    • Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map
    • H. Kang and G. Nakamura, Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map, Inverse Problems, 18 (2002), 1079-1088.
    • (2002) Inverse Problems , vol.18 , pp. 1079-1088
    • Kang, H.1    Nakamura, G.2
  • 16
    • 0000714376 scopus 로고    scopus 로고
    • Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
    • A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), 1489-1512.
    • (1998) Inverse Problems , vol.14 , pp. 1489-1512
    • Kirsch, A.1
  • 17
    • 0000505016 scopus 로고    scopus 로고
    • New characterizations of solutions in inverse scattering theory
    • A. Kirsch, New characterizations of solutions in inverse scattering theory, Applicable Analysis, 76 (2000), 319-350.
    • (2000) Applicable Analysis , vol.76 , pp. 319-350
    • Kirsch, A.1
  • 19
    • 4544220701 scopus 로고    scopus 로고
    • Identification of a temperature dependent heat conductivity from single boundary measurements
    • P. Kügler, Identification of a temperature dependent heat conductivity from single boundary measurements, SIAM J. Num. Anal., 41 (2003), 1543-1563.
    • (2003) SIAM J. Num. Anal , vol.41 , pp. 1543-1563
    • Kügler, P.1
  • 20
    • 0034381292 scopus 로고    scopus 로고
    • Self-guided waves and exact solutions of the nonlinear Helmholtz equation
    • T. A. Laine and A. T. Friberg, Self-guided waves and exact solutions of the nonlinear Helmholtz equation, J. Opt. Soc. Am. B Opt. Phys., 17 (2000), 751-757.
    • (2000) J. Opt. Soc. Am. B Opt. Phys , vol.17 , pp. 751-757
    • Laine, T.A.1    Friberg, A.T.2
  • 21
    • 54749107179 scopus 로고    scopus 로고
    • Recovering an obstacle and a nonlinear conductivity from Cauchy data
    • W. Rundell, Recovering an obstacle and a nonlinear conductivity from Cauchy data, Inverse Problems, 24 (2008), 12 pp.
    • (2008) Inverse Problems , vol.24 , pp. 12
    • Rundell, W.1
  • 22
    • 44949099337 scopus 로고    scopus 로고
    • A uniqueness theorem and reconstruction of singularities for a twodimensional nonlinear Schrödinger equation
    • V. Serov and M. Harju, A uniqueness theorem and reconstruction of singularities for a twodimensional nonlinear Schrödinger equation, Nonlinearity, 21 (2008), 1323-1337.
    • (2008) Nonlinearity , vol.21 , pp. 1323-1337
    • Serov, V.1    Harju, M.2
  • 23
    • 34249719455 scopus 로고    scopus 로고
    • Inverse born approximation for the nonlinear two-dimensional Schrödinger operator
    • V. Serov, Inverse born approximation for the nonlinear two-dimensional Schrödinger operator, Inverse Problems, 23 (2007), 1259-1270.
    • (2007) Inverse Problems , vol.23 , pp. 1259-1270
    • Serov, V.1
  • 24
    • 0000087330 scopus 로고    scopus 로고
    • On a quasilinear inverse boundary value problem
    • Z. Sun, On a quasilinear inverse boundary value problem, Mathematische Zeitschrift, 221 (1996), 293-305.
    • (1996) Mathematische Zeitschrift , vol.221 , pp. 293-305
    • Sun, Z.1
  • 25
    • 23044531521 scopus 로고    scopus 로고
    • Inverse scattering for the nonlinear Schrödinger equation. II. Reconstruction of the potential and the nonlinearity in the multidimensional case
    • R. Weder, Inverse scattering for the nonlinear Schrödinger equation. II. Reconstruction of the potential and the nonlinearity in the multidimensional case, Proc. Amer. Math. Soc., 129 (2001), 3637-3645.
    • (2001) Proc. Amer. Math. Soc , vol.129 , pp. 3637-3645
    • Weder, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.