Free Access
Issue
ESAIM: COCV
Volume 11, Number 1, January 2005
Page(s) 1 - 56
DOI https://doi.org/10.1051/cocv:2004030
Published online 15 December 2004
  1. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30 (1992) 1024-1065. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Bellassoued, Distribution of resonances and decay of the local energy for the elastic wave equations. Comm. Math. Phys. 215 (2000) 375-408. [Google Scholar]
  3. M. Bellassoued, Carleman estimates and decay rate of the local energy for the Neumann problem of elasticity. Progr. Nonlinear Differ. Equations Appl. 46 (2001) 15-36. [Google Scholar]
  4. M. Bellassoued, Unicité et contrôle pour le système de Lamé. ESAIM: COCV 6 (2001) 561-592. [CrossRef] [EDP Sciences] [Google Scholar]
  5. L. Baudouin and J.-P. Puel, Uniqueness and stability in an inverse problem for the Schrödinger equation. Inverse Problems 18 (2002) 1537-1554. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  6. A.L. Bukhgeim, Introduction to the Theory of Inverse Problems. VSP, Utrecht (2000). [Google Scholar]
  7. A.L. Bukhgeim, J. Cheng, V. Isakov and M. Yamamoto, Uniqueness in determining damping coefficients in hyperbolic equations, in Analytic Extension Formulas and their Applications, Kluwer, Dordrecht (2001) 27-46. [Google Scholar]
  8. A.L. Bukhgeim and M.V. Klibanov, Global uniqueness of a class of multidimensional inverse problems. Soviet Math. Dokl. 24 (1981) 244-247. [Google Scholar]
  9. T. Carleman, Sur un problème d'unicité pour les systèmes d'équations aux derivées partielles à deux variables independantes. Ark. Mat. Astr. Fys. 2B (1939) 1-9. [Google Scholar]
  10. B. Dehman and L.Robbiano, La propriété du prolongement unique pour un système elliptique. Le système de Lamé. J. Math. Pures Appl. 72 (1993) 475-492. [MathSciNet] [Google Scholar]
  11. G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics. Springer-Verlag, Berlin (1976). [Google Scholar]
  12. Yu.V. Egorov, Linear Differential Equations of Principal Type. Consultants Bureau New York (1986). [Google Scholar]
  13. M. Eller, V. Isakov, G. Nakamura and D. Tataru, Uniqueness and stability in the Cauchy problem for Maxwell's and the elasticity system, in Nonlinear Partial Differential Equations, Vol. 14, Collège de France Seminar, Elsevier-Gauthier Villars. Ser. Appl. Math. 31 (2002) 329-350. [Google Scholar]
  14. M.E. Gurtin, The Linear Theory of Elasticity, in Encyclopedia of Physics, Vol. VIa/2, Mechanics of Solids II, C. Truesdell Ed., Springer-Verlag, Berlin (1972). [Google Scholar]
  15. L. Hörmander, Linear Partial Differential Operators. Springer-Verlag, Berlin (1963). [Google Scholar]
  16. M. Ikehata, G. Nakamura and M. Yamamoto, Uniqueness in inverse problems for the isotropic Lamé system. J. Math. Sci. Univ. Tokyo 5 (1998) 627-692. [MathSciNet] [Google Scholar]
  17. O. Imanuvilov, Controllability of parabolic equations. Mat. Sbornik 6 (1995) 109-132. [Google Scholar]
  18. O. Imanuvilov, On Carleman estimates for hyperbolic equations. Asymptotic Analysis (2002) 32 185-220. [Google Scholar]
  19. O. Imanuvilov, V. Isakov and M. Yamamoto, An inverse problem for the dynamical Lamé system with two sets of boundary data. Commun. Pure Appl. Math. 56 (2003) 1366-1382. [CrossRef] [Google Scholar]
  20. O. Imanuvilov, V. Isakov and M. Yamamoto, New realization on the pseudoconvexity and its application to an inverse problem (preprint). [Google Scholar]
  21. O. Imanuvilov and M. Yamamoto, Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Problems 14 (1998) 1229-1245. [CrossRef] [MathSciNet] [Google Scholar]
  22. O. Imanuvilov and M. Yamamoto, Global Lipschitz stability in an inverse hyperbolic problem by interior observations. Inverse Problems 17 (2001) 717-728. [CrossRef] [MathSciNet] [Google Scholar]
  23. O. Imanuvilov and M. Yamamoto, Global uniqueness and stability in determining coefficients of wave equations. Commun. Partial Differ. Equations 26 (2001) 1409-1425. [CrossRef] [Google Scholar]
  24. O. Imanuvilov and M. Yamamoto, Determination of a coefficient in an acoustic equation with a single measurement. Inverse Problems 19 (2003) 151-171. [Google Scholar]
  25. O. Imanuvilov and M. Yamamoto, Remarks on Carleman estimates and controllability for the Lamé system. Journées Équations aux Dérivées Partielles, Forges-les-Eaux, 3-7 juin 2002, GDR 2434 (CNRS) 1-19. [Google Scholar]
  26. O. Imanuvilov and M. Yamamoto, Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations. Publ. Res. Inst. Math. Sci. 39 (2003) 227-274. [CrossRef] [MathSciNet] [Google Scholar]
  27. O. Imanuvilov and M. Yamamoto, Carleman estimate for a stationary isotropic Lamé system and the applications. Appl. Anal. 83 (2004) 243-270. [CrossRef] [MathSciNet] [Google Scholar]
  28. V. Isakov, A nonhyperbolic Cauchy problem for Formula and its applications to elasticity theory. Comm. Pure Appl. Math. 39 (1986) 747-767. [CrossRef] [MathSciNet] [Google Scholar]
  29. V. Isakov, Inverse Source Problems. American Mathematical Society, Providence, Rhode Island (1990). [Google Scholar]
  30. V. Isakov, Inverse Problems for Partial Differential Equations. Springer-Verlag, Berlin (1998). [Google Scholar]
  31. V. Isakov and M. Yamamoto, Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems. Contem. Math. 268 (2000) 191-225. [Google Scholar]
  32. M.A. Kazemi and M.V. Klibanov, Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities. Appl. Anal. 50 (1993) 93-102. [CrossRef] [MathSciNet] [Google Scholar]
  33. A. Khaĭdarov, Carleman estimates and inverse problems for second order hyperbolic equations. Math. USSR Sbornik 58 (1987) 267-277. [CrossRef] [Google Scholar]
  34. A. Khaĭdarov, On stability estimates in multidimensional inverse problems for differential equations. Soviet Math. Dokl. 38 (1989) 614-617. [MathSciNet] [Google Scholar]
  35. M.V. Klibanov, Inverse problems and Carleman estimates. Inverse Problems 8 (1992) 575-596. [CrossRef] [MathSciNet] [Google Scholar]
  36. H. Kumano-go, Pseudo-differential Operators. MIT Press, Cambrige (1981). [Google Scholar]
  37. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories. Cambridge University Press, Cambridge (2000). [Google Scholar]
  38. J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin (1971). [Google Scholar]
  39. J.L. Lions, Contrôlabilité exacte perturbations et stabilisation de systèmes distribués. Masson, Paris (1988). [Google Scholar]
  40. J.-P. Puel and M. Yamamoto, On a global estimate in a linear inverse hyperbolic problem. Inverse Problems 12 (1996) 995-1002. [CrossRef] [MathSciNet] [Google Scholar]
  41. J.-P. Puel and M. Yamamoto, Generic well-posedness in a multidimensional hyperbolic inverse problem. J. Inverse Ill-posed Problems 5 (1997) 55-83. [CrossRef] [Google Scholar]
  42. L. Rachele, An inverse problem in elastodynamics: uniqueness of the wave speeds in the interior. J. Differ. Equations 162 (2000) 300-325. [CrossRef] [Google Scholar]
  43. A. Ruiz, Unique continuation for weak solutions of the wave equation plus a potential. J. Math. Pures. Appl. 71 (1992) 455-467. [MathSciNet] [Google Scholar]
  44. D. Tataru, Carleman estimates and unique continuation for solutions to boundary value problems. J. Math. Pures. Appl. 75 (1996) 367-408. [MathSciNet] [Google Scholar]
  45. D. Tataru, A priori estimates of Carleman's type in domains with boundary. J. Math. Pures. Appl. 73 (1994) 355-387. [MathSciNet] [Google Scholar]
  46. M. Taylor, Pseudodifferential Operators. Princeton University Press, Princeton, New Jersey (1981). [Google Scholar]
  47. M. Taylor, Pseudodifferential Operators and Nonlinear PDE. Birkhäuser, Boston (1991). [Google Scholar]
  48. V.G. Yakhno, Inverse Problems for Differential Equations of Elasticity. Nauka, Novosibirsk (1990). [Google Scholar]
  49. K. Yamamoto, Singularities of solutions to the boundary value problems for elastic and Maxwell's equations. Japan J. Math. 14 (1988) 119-163. [MathSciNet] [Google Scholar]
  50. M. Yamamoto, Uniqueness and stability in multidimensional hyperbolic inverse problems. J. Math. Pures Appl. 78 (1999) 65-98. [CrossRef] [MathSciNet] [Google Scholar]
  51. X. Zhang, Explicit observability inequalities for the wave equation with lower order terms by means of Carleman inequalities. SIAM J. Control Optim. 39 (2001) 812-834. [CrossRef] [MathSciNet] [Google Scholar]
  52. C. Zuily, Uniqueness and Non-uniqueness in the Cauchy Problem. Birkhäuser, Boston, Basel, Berlin, (1983). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.