Determination of a coefficient in the wave equation with a single measurement

References

• Bugheim , AL and Klibanov , MV . 1981 . Global uniqueness of class of multidimentional inverse problems . Soviet Math. Dokl. , 24 : 244 – 247 .
   Google Scholar
• Klibanov , MV . 1992 . Inverse problems and Carleman estimates . Inverse Probl. , 8 : 575 – 596 .
   Web of Science ®Google Scholar
• Klibanov , MV and Timonov , AA . 2004 . Carleman Estimates for Coefficient Inverse Problems and Numerical Applications , Utrecht : VSP .
   Google Scholar
• Isakov , V . 1998 . Inverse Problems for Partial Differential Equations , Berlin : Springer-Verlag .
   Google Scholar
• Lavrent'ev , MM . 1967 . Some Improperly Posed Problems of Mathematical Physics , Berlin : Springer-Verlag .
   Google Scholar
• Bellassoued , M . 2004 . Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation withvariable coefficients . Appl. Anal. , 83 : 983 – 1014 .
   Google Scholar
• Khaidarov , A . 1989 . On stability estimates in multidimentional inverse problems for differential equation . Soviet Math. Dokl. , 38 : 614 – 617 .
   Google Scholar
• Lasiecka , I , Triggiani , R and Peng-Fei , Yao . 1999 . Inverse/observability estimates for second order hyperbolic equations with variablescoefficients . J. Math. Anal. Appl. , 235 : 13 – 57 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu . 2002 . On Carleman estimates for hyperbolic equations . Asymptotic Anal. , 32 : 185 – 220 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2003 . Determination of a coefficient in an acoustic equation with a single measurement . Inverse Probl. , 19 : 157 – 171 .
   Web of Science ®Google Scholar
• Klibanov , MV and Yamamoto , M . 2006 . Lipschitz stability of an inverse problem for an acoustic equation . Appl. Anal. , 85 : 515 – 538 .
   Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2001 . Global uniqueness and stability in determining coefficients of wave equations . Commun. Partial Differ. Equ. , 26 : 1409 – 1425 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2001 . Global Lipschitz stability in an inverse hyperbolic problem by interior observations . Inverse Probl. , 17 : 717 – 728 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu , Isakov , V and Yamamoto , M . 2003 . An inverse problemfor the dynamical Lamé system with two sets of boundary data . Commun. Pur. Appl. Math. , 56 : 1366 – 1382 .
   Web of Science ®Google Scholar
• Isakov , V and Yamamoto , M . 2000 . Carleman estimate with the Neumann boundary condition and its applications to the observabilityinequality and inverse hyperbolic problems . Contemp. Math. , 268 : 191 – 225 .
   Google Scholar
• Amirov , AKh and Yamamoto , M . 2005 . The time-like Cauchy problem and the inverse problem . Dokl. Akad. Nauk , 402 : 7 – 9 .
   Google Scholar
• Romanov , VG . 2006 . Carleman estimates for a second-order hyperbolic equation . Siberian Math. J. , 47 : 135 – 151 .
   Web of Science ®Google Scholar
• Lebeau , G . 1996 . “ Equation des ondes amorties ” . In Algebraic and Geometric Methods in Mathematical Physics , Edited by: Boutet de Monvel , A and Marchenko , V . 73 – 109 . The Netherlands : Kluwer Academic .
   Google Scholar
• Lebeau , G and Robbiano , L . 1997 . Stabilisation del'équation des ondes par le bord . Duke Math. J. , 86 : 465 – 491 .
   Web of Science ®Google Scholar
• Albano , P and Tataru , D . 2000 . Carleman estimates and boundary observability for a coupled parabolic-hyperbolic system . Elect. J. Differ. Equ. , 22 : 1 – 15 .
   Google Scholar
• Tataru , D . Carleman estimates, unique continuation andapplications Preprint
   Google Scholar
• Tataru , D . 1996 . Carleman estimates and uniquecontinuation for solutions to boundary value problems . J. Math. Pures Appl. , 75 : 367 – 408 .
   Web of Science ®Google Scholar
• Lasiecka , I and Tataru , D . 1993 . Uniform boundary stabilization of semilinear wave equations with boundary damping . Differ. Integral Equ. , 6 : 507 – 533 .
   Google Scholar