Determination of point sources in vibrating plate by boundary measurements

References

• Bruckner , G and Yamamoto , M . 2000 . Determination of point wave sources by pointwise observations: Stability and reconstruction . Inverse Probl. , 16 : 723 – 748 .
   Web of Science ®Google Scholar
• Yamamoto , M . 1995 . Stability, reconstruction and regularization for an inverse source hyperbolic problem by a control method . Inverse Probl. , 11 : 481 – 496 .
   Web of Science ®Google Scholar
• Yamamoto , M . 1996 . Determination of forces in vibrations of beams and plates by pointwise and line observations . J. Inverse Ill-Posed Probl. , 4 : 437 – 457 .
   Google Scholar
• Komornik , V and Yamamoto , M . 2005 . Estimation of point sources and applications to inverse problems . Inverse Probl. , 21 ( 6 ) : 2051 – 2070 .
   Web of Science ®Google Scholar
• Lions , J-L . 1988 . Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome 1 , Vol. 8 , Paris : Masson .
   Google Scholar
• Komornik , V and Yamamoto , M . 2002 . Upper and lower estimates in determining point sources in a wave equation . Inverse Probl. , 18 : 319 – 329 .
   Web of Science ®Google Scholar
• Nicaise , S and Zaïr , O . 2003 . Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees . Rev. Mat. Univ. Complutense Madrid , 16 : 1 – 28 .
   Google Scholar
• Yamamoto , M . 1994 . Well-posedness of an inverse hyperbolic problem by the Hilbert uniqueness method . J. Inverse Ill-Posed Probl. , 2 : 349 – 368 .
   Google Scholar
• Nicaise , S and Zaïr , O . 2004 . Identifiability, stability and reconstruction results of point sources by boundary measurements . Electron. J. Differ. Eqns , 20 : 1 – 17 .
   Google Scholar
• G. Bruckner and M. Yamamoto, Identification of point sources by boundary observations: uniqueness, stability and reconstruction, in Hermis' 96, Proceedings of the Third Hellenic European Conference on Mathematics and Informatics, E.A. Lipitakis ed., Athens, LEA, 1997, pp. 154–161
   Google Scholar
• Komornik , V . 1994 . Exact Controllability and Stabilization, the Multiplier Method , Vol. 36 , Paris : Masson .
   Google Scholar
• Klibanov , MV and Malinsky , J . 1991 . Newton–Kantorovich method for 3-dimensional potential inverse scattering problem and stability for hyperbolic Cauchy problem with time data . Inverse Prob. , 7 : 577 – 596 .
   Web of Science ®Google Scholar
• Clason , C and Klibanov , MV . 2007 . The quasi-reversibility method for thermoacoustic tomography in a heterogeneous medium . SIAM J. Sci. Comp. , 30 : 1 – 23 .
   Web of Science ®Google Scholar
• Klibanov , MV . 2005 . Lipschitz stability for hyperbolic inequalities in octants with the lateral Cauchy data and refocusing in time reversal . J. Inverse Ill-Posed Probl. , 13 : 353 – 363 .
   Google Scholar
• Klibanov , MV and Timonov , A . 2004 . Carleman Estimates for Coefficient Inverse Problem and Numerical Application , Utrecht , , The Netherlands : VSP .
   Google Scholar
• Kazemi , M and Klibanov , MV . 1993 . Stability estimates for ill-posed Cauchy problem involving hyperbolic equation and inequalities . Appl. Anal. , 50 : 93 – 102 .
   Google Scholar
• Klibanov , MV , Kuzhuget , AV , Kabanikhin , SI and Nechaev , DV . 2008 . A new version of the quasi-reversibility method for the thermacoustic tomography and a coefficient inverse problem . Appl. Anal. , 87 : 1227 – 1254 .
   Web of Science ®Google Scholar
• Klibanov , MV and Rakesh . 1992 . Numerical solution of a timelike Cauchy problem for the wave equation . Math. Meth. Appl. Sci. , 15 : 559 – 570 .
   Web of Science ®Google Scholar