Lipschitz stability in the lateral Cauchy problem for elasticity system

Kyoto Journal of Mathematics

Volumn 43, Issue 3, 2003, Pages 475-501

  Cheng, Jin ^a   Isakov, Victor ^b   Yamamoto, Masahiro ^c   Zhou, Qi ^d  

^a FUDAN UNIVERSITY   (China)

^b WICHITA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF TOKYO   (Japan)

^d IBM JAPAN LTD   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1942508080     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250283691     Document Type: Article

References (28)

1. F. Alabau and V. Komornik, Observabilité, contrôlabilité et stabilisation frontière du système d'élasticité linéare, C. R. Acad. Sci. Paris Sér. I. Math. 324 (1997), 519-524.
2. D. D. Ang, M. Ikehata, D. D. Trong and M. Yamamoto, Unique continuation for a stationary isotropic Lamé system with variable coefficients, Comm. Partial Differential Equations 23 (1998), 371-385.
3. 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.
4. A. Bukhgeim and V. Kardakov, Solution of the inverse problem for the equation of elastic waves by the method of spherical means, Siberian Math. J. 19 (1978), 528-535.
5. N. Burq, Contrôlabilité exacte des ondes dans des ouverts peu réguliers, Asymptot. Anal. 14 (1997), 157-191.
6. 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.
7. M. Eller, V. Isakov, G. Nakamura and D. Tataru, Uniqueness and stability in the Cauchy problem for Maxwell and elasticity systems, Stud. Math. Appl. 31, Elsevier, Amsterdam, 2002, pp. 329-349.
8. M. Grasselli and M. Yamamoto, Identifying a spatial body force in linear elastodynamics via traction measurements, SIAM J. Control Optim. 36 (1998), 1190-1206.
9. L. Hörmander, Linear Partial Differential Operators, Springer-Verlag, Berlin, 1963.
10. _, The Analysis of Linear Partial Differential Operators I-IV, Springer-Verlag, Berlin, 1983.
11. M. A. Horn, Implication of sharp trace regularity results on boundary stabilization of the system of linear elasticity, J. Math. Anal. Appl. 223 (1998), 126-150.
12. 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.
13. c and its applications to elasticity theory, Comm. Pure Appl. Math. 39 (1986), 747-767.
14. _, Inverse Problems for Partial Differential Equations, Springer-Verlag, Berlin, 1998.
15. F. John, Partial Differential Equations, Springer-Verlag, Berlin, 1986.
16. M. V. Klibanov and J. Malinsky, Newton-Kantorowich method for three-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time-dependent data, Inverse problems 7 (1991), 577-596.
17. V. Komornik, Exact Controllability and Stabilization, the Multiplier Method, Masson, Paris, 1994.
18. I. Lasiecka, J.-L. Lions and R. Triggiani, Non-homogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures Appl. 65 (1986), 149-192.
19. I. Lasiecka and R. Triggiani, Carleman estimates and exact boundary controllability for a system of coupled, nonconservative second-order hyperbolic equations, In: Partial Differential Equation Methods in Control and Shape Analysis, Lecture Notes in Pure Appl. Math. 188, Marcel Dekker, Inc., New York, 1997, pp. 215-243.
20. M. M. Lavrent'ev, V. G. Romanov and S. P. Shishat-skiǐ, Ill-posed Problems of Mathematical Physics and Analysis, English translation of the original Russian version in 1980, American Mathematical Society, Providence, Rhode Island, 1986.
21. G. Lebeau and E. Zuazua, Null-controllability of a system of linear thermoelasticity, Arch. Rational Mech. Anal. 141 (1998), 297-329.
22. Lop Fat Ho, Observabilité frontière de l'équation des ondes, C. R. Acad. Sci. Paris Sér. I. Math. 302 (1986), 443-446.
23. J. Powell, An unconditional estimate for solutions of a wave equation, J. Math. Anal. Appl. 179 (1993), 179-186.
24. R. Sakamoto, Mixed problems for hyperbolic equations, I. Energy inequalities, J. Math. Kyoto Univ. 10 (1970), 349-373.
25. D. Tataru, Unique continuation for solutions to PDE's; between Hörmander's theorem and Holmgren's theorem, Comm. Partial Differential Equations 20 (1995), 855-884.
26. _, Boundary controllability for conservative PDEs, Appl. Math. Optim. 31 (1995), 257-295.
27. _, Carleman estimates and unique continuation for solutions to boundary value problems, J. Math. Pures Appl. 75 (1996), 367-408.
28. M. Yamamoto, On an inverse problem of determining source terms in Maxwell's equations with a single measurement, In: Inverse Problems, Tomography, and Image Processing, Plenum Press, New York, 1998, pp. 241-256.