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Original Articles

Lipschitz stability in an inverse problem for a hyperbolic equation with a finite set of boundary data

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Pages 1105-1119 | Received 04 Apr 2008, Accepted 06 Jul 2008, Published online: 23 Dec 2008

References

  • Jellali , D . 2006 . An inverse problem for the acoustic wave equation with finite sets of boundary data . J. Inverse Ill-Posed Prob. , 14 : 665 – 684 .
  • Yuan , G and Yamamoto , M . Lipschitz stability in the determination of the principal part of a parabolic equation, to appear in ESAIM:COCV .
  • Bellassoued , M . 2004 . Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients . Appl. Anal. , 83 : 983 – 1014 .
  • Bellassoued , M . 2004 . Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation . Inverse Prob. , 20 : 1033 – 1052 .
  • Bellassoued , M and Yamamoto , M . 2008 . Determination of a coefficient in the wave equation with a single measurement . Appl. Anal. , 87 : 901 – 920 .
  • Bellassoued , M and Yamamoto , M . 2006 . Logarithmic stability in determination of coefficient in acoustic equation by arbitrary boundary observation . J. Math. Pures et App. , 85 : 193 – 224 .
  • Imanuvilov , OYu and Yamamoto , M . 1998 . Lipschitz stability in inverse parabolic problems by the Carleman estimate . Inverse Prob. , 14 : 1229 – 1245 .
  • Imanuvilov , OYu and Yamamoto , M . 2001 . Global uniqueness and stability in determining coefficients of wave equations . Comm. Partial Diff. Equ. , 26 : 1409 – 1425 .
  • Imanuvilov , OYu and Yamamoto , M . 2001 . Global Lipschitz stability in an inverse hyperbolic problem by interior observations . Inverse Prob. , 17 : 717 – 728 .
  • Imanuvilov , OYu and Yamamoto , M . 2003 . Determination of a coefficient in an acoustic equation with a single measurement . Inverse Prob. , 19 : 157 – 171 .
  • Isakov , V . 1986 . A nonhyperbolic Cauchy problems for □ b □ c and its applications to elasticity theory . Comm. Pur. Appl. Math. , 39 : 747 – 767 .
  • Khaĭdarov , A . 1987 . Carleman estimates and inverse problems for second order hyperbolic equations . Math. USSR SB+ , 58 : 267 – 277 .
  • Khaĭdarov , A . 1989 . On stability estimates in multidimensional inverse problems for differential equations . Soviet Math. Dokl. , 38 : 614 – 617 .
  • Klibanov , MV and Yamamoto , M . 2006 . Lipschitz stability of an inverse problem for an acoustic equation . Appl. Anal. , 85 : 515 – 538 .
  • Kubo , M . 2000 . Uniqueness in inverse hyperbolic problems-Carleman estimates for boundary value problems . J. Math. Kyoto Univ. , 40 : 451 – 473 .
  • Puel , J-P and Yamamoto , M . 1996 . On a global estimate in a linear inverse hyperbolic problem . Inverse Prob. , 12 : 995 – 1002 .
  • Yamamoto , M . 1999 . Uniqueness and stability in multidimensional hyperbolic inverse problems . J. Math. Pures App. , 78 : 65 – 98 .
  • Bukhgeim , AL and Klibanov , MV . 1981 . Global uniqueness of a class of multidimensional inverse problems . Soviet Math. Dokl. , 24 : 244 – 247 .
  • Isakov , V . 1998 . Inverse Problems for Partial Differential Equations , Berlin : Springer-Verlag .
  • Klibanov , MV . 1992 . Inverse problems and Carleman estimates . Inverse Prob. , 8 : 575 – 596 .
  • Klibanov , MV . 2000 . “ Carleman estimates and inverse problems in the last two decades ” . In Surveys on Solution Methods for Inverse Problems , Edited by: Colton , D , Engl , HW , Louis , AK , McLaughlin , JR and Rundell , W . 119 – 146 . Wien : Springer-Verlag .
  • Klibanov , MV and Timonov , AA . 2004 . Carleman Estimates for Coefficient Inverse Problems and Numerical Applications , Utrecht : VSP .
  • Bardos , C , Lebeau , G and Rauch , J . 1992 . Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary . SIAM J. Control Optim. , 30 : 1024 – 1065 .
  • Kazemi , MA and Klibanov , MV . 1993 . Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities . Appl. Anal. , 50 : 93 – 102 .
  • Klibanov , MV and Malinsky , J . 1991 . Newton-Kantorovich method for three-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time-dependent data . Inverse Prob. , 7 : 577 – 596 .
  • Imanuvilov , OYu . 2002 . On Carleman estimates for hyperbolic equations . Aymptotic Anal. , 32 : 185 – 220 .

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