An inverse source problem for the Lamé system with variable coefficients

References

• Aki K Richards PG 1980 Quantitative Seismology Theory and Methods I New York Freeman
   Google Scholar
• Alabau , F and Komornik , V . 1997 . Observabilité, contrôlabilité et stabilisation frontière du systéme d'élasticité linèaire . Comptes Rendus de l'Academie des Sciences. Mathematique , 324 : 519 – 524 .
   Google Scholar
• Alabau , F and Komornik , V . 1999 . Boundary observability and controllability of linear elastodynamics systems . SIAM Journal on Control and Optimization , 37 : 521 – 542 .
   Web of Science ®Google Scholar
• Cheng , J , Isakov , V , Yamamoto , M and Zhou , Q . 2003 . Lipschitz stability in the lateral Cauchy problem for elasticity system . Journal of Mathematics of Kyoto University , 43 : 475 – 501 .
   Google Scholar
• Grasselli , M and Yamamoto , M . 1998 . Identifying a spatial body force in linear elastodynamics via traction measurements . SIAM Journal on Control and Optimization , 36 : 1190 – 1206 .
   Web of Science ®Google Scholar
• Grasselli , M , Ikehata , M and Yamamoto , M . 2000 . Direct and inverse inequalities for the isotropic Lamé system with variable coefficients . Comptes Rendus de l'Academie des Sciences. Mecanique , 328 : 575 – 580 .
   Google Scholar
• Guesmia , A . 1998 . On linear elasticity systems with variable coefficients . Kyushu Journal of Mathematics , 52 : 227 – 248 .
   Google Scholar
• Gurtin ME 1984 The Linear Theory of Elasticity Mechanics of Solids II C. Truesdell (Ed.) Berlin Springer-Verlag
   Google Scholar
• Ho , LF . 1986 . Observabilité frontière de l'équation des ondes . Comptes Rendus de l'Academie des Sciences. Mathematique , 302 : 443 – 446 .
   Google Scholar
• Imanuvilov , Oleg , Yu. and Yamamoto , M . Carleman estimates for the non-stationary Lamé system and the application to an inverse problem . ESAIM. Control, Optimisation and Calculus of Variations , 11 1 – 56 .
   Google Scholar
• Komornik V 1994 Exact Controllability and Stabilization: the Multiplier Method Chichester John Wiley & Sons
   Google Scholar
• Lasiecka , I , Lions , J-L and Triggiani , R . 1986 . Nonhomogeneous boundary value problems for second order hyperbolic operators . Journal de Mathematiques Pures et Appliquees. Neuvieme Serie , 65 : 149 – 192 .
   Web of Science ®Google Scholar
• Lasiecka , I and Triggiani , R . 1989 . Exact controllability of the wave equation with Neumann boundary control . Applied Mathematics and Optimization. An International Journal with Applications to Stochastics , 19 : 243 – 290 .
   Web of Science ®Google Scholar
• Lasiecka , I and Triggiani , R . 2002 . Uniform stabilization of a shallow shell model with nonlinear boundary feedbacks . Journal of Mathematical Analysis and Applications , 269 : 642 – 688 .
   Google Scholar
• Lions J-L 1988 Contrôlabilité Exacte Perturbations et Stabilisation de Systèmes Distribués 1 Masson Paris
   Google Scholar
• Nicaise , S . 1993 . About the Lamé systems in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation II: exact controllability . Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV , 20 : 163 – 191 .
   Google Scholar
• Telega JJ Bielski WR 1996 Exact controllability of anisotropic elastic bodies In: K. Malanowski, Z. Nahorski, Z. and M. Peszyńska (Eds) Modelling and Optimization of Distributed Parameter Systems Applications to Engineering, Chapman & Hall London pp. 254–262
   Google Scholar
• Telega JJ Bielski WR 1999 On two problems of exact controllability for elastic anisotropic solids In: J. Holnicki-Szulc and J. Rodellar (Eds) Smart Structures, Kluwer Dordrecht pp. 345–354
   Google Scholar
• Triggiani , R . 1988 . Exact boundary controllability on L 2(Ω) × H −1(Ω) of the wave equation with Dirichlet boundary control acting on a portion of the boundary ∂Ω, and related problems . Applied Mathematics and Optimization. An International Journal with Applications to Stochastics , 18 : 241 – 277 .
   Web of Science ®Google Scholar
• Yamamoto , M . 1995 . Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method . Inverse Problems , 11 : 481 – 496 .
   Web of Science ®Google Scholar