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Volumn 260, Issue 5, 2016, Pages 4786-4804

Increasing stability in the inverse source problem with many frequencies

Author keywords

Increasing stability; Inverse source problems; Multiple frequencies

Indexed keywords


EID: 84949660592     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2015.11.030     Document Type: Article
Times cited : (110)

References (31)
  • 1
    • 0003593314 scopus 로고    scopus 로고
    • Antenna Theory – Analysis and Design
    • Wiley Hoboken, NJ
    • [1] Balanis, C.A., Antenna Theory – Analysis and Design. 2005, Wiley, Hoboken, NJ.
    • (2005)
    • Balanis, C.A.1
  • 2
    • 0036553053 scopus 로고    scopus 로고
    • Inverse source problem for Maxwell's equation in magnetoencephalography
    • [2] Ammari, H., Bao, G., Fleming, J., Inverse source problem for Maxwell's equation in magnetoencephalography. SIAM J. Appl. Math. 62 (2002), 1369–1382.
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1369-1382
    • Ammari, H.1    Bao, G.2    Fleming, J.3
  • 3
    • 0032638277 scopus 로고    scopus 로고
    • Optical tomography in medical imaging
    • [3] Arridge, S., Optical tomography in medical imaging. Inverse Probl. 15 (1999), R41–R93.
    • (1999) Inverse Probl. , vol.15 , pp. R41-R93
    • Arridge, S.1
  • 4
    • 79953654399 scopus 로고    scopus 로고
    • Themoacoustic tomography arising in brain imaging
    • 075011
    • [4] Stefanov, P., Uhlmann, G., Themoacoustic tomography arising in brain imaging. Inverse Probl., 27, 2011, 075011.
    • (2011) Inverse Probl. , vol.27
    • Stefanov, P.1    Uhlmann, G.2
  • 5
    • 0003430391 scopus 로고    scopus 로고
    • Inverse Problems for Partial Differential Equations
    • Springer-Verlag New York
    • [5] Isakov, V., Inverse Problems for Partial Differential Equations. 2006, Springer-Verlag, New York.
    • (2006)
    • Isakov, V.1
  • 6
    • 70450193186 scopus 로고    scopus 로고
    • Acoustic source identification using multiple frequency information
    • 115005
    • [6] Eller, M., Valdivia, N.P., Acoustic source identification using multiple frequency information. Inverse Probl., 25, 2009, 115005.
    • (2009) Inverse Probl. , vol.25
    • Eller, M.1    Valdivia, N.P.2
  • 7
    • 78049297003 scopus 로고    scopus 로고
    • A multi-frequency inverse source problem
    • [7] Bao, G., Lin, J., Triki, F., A multi-frequency inverse source problem. J. Differential Equations 249 (2010), 3443–3465.
    • (2010) J. Differential Equations , vol.249 , pp. 3443-3465
    • Bao, G.1    Lin, J.2    Triki, F.3
  • 8
    • 84871727944 scopus 로고    scopus 로고
    • Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data
    • [8] Bao, G., Lin, J., Triki, F., Numerical solution of the inverse source problem for the Helmholtz equation with multiple frequency data. Contemp. Math. 548 (2011), 45–60.
    • (2011) Contemp. Math. , vol.548 , pp. 45-60
    • Bao, G.1    Lin, J.2    Triki, F.3
  • 9
    • 84966246360 scopus 로고
    • Energy flow: wave motion and geometrical optics
    • [9] Morawetz, C.S., Energy flow: wave motion and geometrical optics. Bull. Amer. Math. Soc. 76 (1970), 661–674.
    • (1970) Bull. Amer. Math. Soc. , vol.76 , pp. 661-674
    • Morawetz, C.S.1
  • 10
    • 84980073634 scopus 로고
    • Continuous dependence on data for solutions of partial differential equations with a prescribed bound
    • [10] John, F., Continuous dependence on data for solutions of partial differential equations with a prescribed bound. Comm. Pure Appl. Math. 13 (1960), 551–587.
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 551-587
    • John, F.1
  • 11
    • 77951995694 scopus 로고    scopus 로고
    • Increasing stability of the continuation for the Maxwell system
    • 074005
    • [11] Aralumallige, S.D., Isakov, V., Increasing stability of the continuation for the Maxwell system. Inverse Probl., 26, 2010, 074005.
    • (2010) Inverse Probl. , vol.26
    • Aralumallige, S.D.1    Isakov, V.2
  • 12
    • 3042528735 scopus 로고    scopus 로고
    • Increased stability in the continuation of solutions to the Helmholtz equation
    • [12] Hrycak, T., Isakov, V., Increased stability in the continuation of solutions to the Helmholtz equation. Inverse Probl. 20 (2004), 697–712.
    • (2004) Inverse Probl. , vol.20 , pp. 697-712
    • Hrycak, T.1    Isakov, V.2
  • 13
    • 84872006751 scopus 로고    scopus 로고
    • Regions of stability in the Cauchy problem for the Helmholtz equation
    • [13] Isakov, V., Kindermann, S., Regions of stability in the Cauchy problem for the Helmholtz equation. Methods Appl. Anal. 18 (2011), 1–30.
    • (2011) Methods Appl. Anal. , vol.18 , pp. 1-30
    • Isakov, V.1    Kindermann, S.2
  • 14
    • 34548693219 scopus 로고    scopus 로고
    • Increased stability in the continuation for the Helmholtz equation with variable coefficient
    • [14] Isakov, V., Increased stability in the continuation for the Helmholtz equation with variable coefficient. Contemp. Math. 426 (2007), 255–269.
    • (2007) Contemp. Math. , vol.426 , pp. 255-269
    • Isakov, V.1
  • 15
    • 77951990301 scopus 로고    scopus 로고
    • Increased stability in the Cauchy problem for some elliptic equations
    • C. Bardos A. Fursikov Springer-Verlag
    • [15] Isakov, V., Increased stability in the Cauchy problem for some elliptic equations. Bardos, C., Fursikov, A., (eds.) Instability in Models Connected with Fluid Flow, 2007, Springer-Verlag, 337–360.
    • (2007) Instability in Models Connected with Fluid Flow , pp. 337-360
    • Isakov, V.1
  • 16
    • 80755150615 scopus 로고    scopus 로고
    • Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map
    • [16] Isakov, V., Increasing stability for the Schrödinger potential from the Dirichlet-to Neumann map. Discrete Contin. Dyn. Syst. Ser. S 4 (2011), 631–641.
    • (2011) Discrete Contin. Dyn. Syst. Ser. S , vol.4 , pp. 631-641
    • Isakov, V.1
  • 17
    • 84924995300 scopus 로고    scopus 로고
    • Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to Neumann map
    • [17] Isakov, V., Wang, J.-N., Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to Neumann map. Inverse Probl. Imaging 8 (2014), 1139–1150.
    • (2014) Inverse Probl. Imaging , vol.8 , pp. 1139-1150
    • Isakov, V.1    Wang, J.-N.2
  • 18
    • 0003511516 scopus 로고    scopus 로고
    • Vector-Valued Laplace Transforms and Cauchy Problems
    • Birkhäuser Basel
    • [18] Arendt, W., Batty, C., Hieber, M., Neubrander, F., Vector-Valued Laplace Transforms and Cauchy Problems. 2011, Birkhäuser, Basel.
    • (2011)
    • Arendt, W.1    Batty, C.2    Hieber, M.3    Neubrander, F.4
  • 19
    • 84957249045 scopus 로고
    • Unique continuation for solutions, to PDE's; between Hörmander's theorem and Holmgren's theorem
    • [19] Tataru, D., Unique continuation for solutions, to PDE's; between Hörmander's theorem and Holmgren's theorem. Comm. Partial Differential Equations 20 (1995), 855–884.
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 855-884
    • Tataru, D.1
  • 20
    • 33847715280 scopus 로고    scopus 로고
    • Bounded Analytic Functions
    • Springer-Verlag New York
    • [20] Garnett, J., Bounded Analytic Functions. 2007, Springer-Verlag, New York.
    • (2007)
    • Garnett, J.1
  • 21
    • 84979864014 scopus 로고
    • General hyperbolic diffraction problems
    • Amer. Math. Soc.
    • [21] Isakov, V., General hyperbolic diffraction problems. Trudy Sobolev Seminar, 1977, Amer. Math. Soc.
    • (1977) Trudy Sobolev Seminar
    • Isakov, V.1
  • 22
    • 0009381238 scopus 로고
    • Mixed problems for hyperbolic equations I, II
    • 403–417
    • [22] Sakamoto, R., Mixed problems for hyperbolic equations I, II. J. Math. Kyoto Univ. 10 (1970), 349–373 403–417.
    • (1970) J. Math. Kyoto Univ. , vol.10 , pp. 349-373
    • Sakamoto, R.1
  • 23
    • 0041946012 scopus 로고    scopus 로고
    • Control Theory for Partial Differential Equations: Continuous and Approximation Theories
    • Cambridge University Press New York
    • [23] Lasiecka, I., Triggiani, R., Control Theory for Partial Differential Equations: Continuous and Approximation Theories. Encyclopedia Math. Appl., vols. 74–75, 2000, Cambridge University Press, New York.
    • (2000) Encyclopedia Math. Appl. , vol.74-75
    • Lasiecka, I.1    Triggiani, R.2
  • 24
    • 0001490384 scopus 로고
    • Observabilite frontiere de l'equation des ondes
    • [24] Ho, L.F., Observabilite frontiere de l'equation des ondes. C. R. Acad. Sci. Paris 302 (1986), 443–446.
    • (1986) C. R. Acad. Sci. Paris , vol.302 , pp. 443-446
    • Ho, L.F.1
  • 25
    • 84937872089 scopus 로고    scopus 로고
    • A recursive algorithm for multi-frequency acoustic inverse source problems
    • [25] Bao, G., Lu, S., Rundell, W., Xu, B., A recursive algorithm for multi-frequency acoustic inverse source problems. SIAM J. Numer. Anal. 53 (2015), 1608–1628.
    • (2015) SIAM J. Numer. Anal. , vol.53 , pp. 1608-1628
    • Bao, G.1    Lu, S.2    Rundell, W.3    Xu, B.4
  • 26
    • 0026923885 scopus 로고
    • Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundaries
    • [26] Bardos, C., Lebeau, J., Rauch, J., Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundaries. SIAM J. Control Optim. 30 (1992), 1024–1065.
    • (1992) SIAM J. Control Optim. , vol.30 , pp. 1024-1065
    • Bardos, C.1    Lebeau, J.2    Rauch, J.3
  • 27
    • 0347940923 scopus 로고
    • Newton–Kantorovich method for 3-dimensional inverse scattering problem and stability of the hyperbolic Cauchy problem with time independent data
    • [27] Klibanov, M.M., Newton–Kantorovich method for 3-dimensional inverse scattering problem and stability of the hyperbolic Cauchy problem with time independent data. Inverse Probl. 7 (1991), 577–595.
    • (1991) Inverse Probl. , vol.7 , pp. 577-595
    • Klibanov, M.M.1
  • 28
    • 0000863910 scopus 로고
    • Boundary controllability for conservative PDE's
    • [28] Tataru, D., Boundary controllability for conservative PDE's. Appl. Math. Optim. 31 (1995), 257–295.
    • (1995) Appl. Math. Optim. , vol.31 , pp. 257-295
    • Tataru, D.1
  • 29
    • 77956816816 scopus 로고    scopus 로고
    • Uniqueness and stability in the Cauchy problem for Maxwell' and elasticity systems
    • D. Cioranescu J.-L. Lions North-Holland, Elsevier Science
    • [29] Eller, M., Isakov, V., Nakamura, G., Tataru, D., Uniqueness and stability in the Cauchy problem for Maxwell' and elasticity systems. Cioranescu, D., Lions, J.-L., (eds.) Nonlinear Partial Differential Equations and Their Applications, 2002, North-Holland, Elsevier Science, 329–351.
    • (2002) Nonlinear Partial Differential Equations and Their Applications , pp. 329-351
    • Eller, M.1    Isakov, V.2    Nakamura, G.3    Tataru, D.4
  • 30
    • 84979858023 scopus 로고    scopus 로고
    • On increasing stability in the Cauchy problem for general elliptic equations
    • A. Favini et al. (eds.) North-Holland, Elsevier Science, Springer-Verlag (Ch. 10)
    • [30] Isakov, V., On increasing stability in the Cauchy problem for general elliptic equations. Favini, A., et al. (eds.) New Prospects in Direct, Inverse, and Control Problems for Evolution Equations Springer INdAM Ser., 2014, North-Holland, Elsevier Science, Springer-Verlag (Ch. 10).
    • (2014) New Prospects in Direct, Inverse, and Control Problems for Evolution Equations, Springer INdAM Ser.
    • Isakov, V.1
  • 31
    • 84908503263 scopus 로고    scopus 로고
    • Sensitivity analysis of an inverse problem for the wave equations in the presence of caustics
    • [31] Bao, G., Zhang, H., Sensitivity analysis of an inverse problem for the wave equations in the presence of caustics. J. Amer. Math. Soc. 27 (2014), 953–981.
    • (2014) J. Amer. Math. Soc. , vol.27 , pp. 953-981
    • Bao, G.1    Zhang, H.2


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