Open Access
Volume 29, 2023
Article Number 88
Number of page(s) 29
Published online 20 December 2023
  1. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient condition for the observation, control, and stabilization of waves from the boundary. SIAM J. Control. Optim. 30 (1992) 1024–1065. [CrossRef] [MathSciNet] [Google Scholar]
  2. L. Baudouin, M. Buhan and S. Ervedoza, Global Carleman estimates for waves and applications. Commun. Partial Diff. Equ. 38 (2013) 823–859. [CrossRef] [Google Scholar]
  3. X. Fu, Q. Lü and X. Zhang, Carleman Estimates for Second Order Partial Differential Operators and Applications. Springer (2019). [CrossRef] [Google Scholar]
  4. M.M. Lavent’ev, V.G. Romanov and S.P. Shishat·skii, Ill-Posed Problems of Mathematical Physics and Analysis. American Mathematical Society, Providence (1986). [Google Scholar]
  5. X. Li and J. Yong, Optimal Control Theory for Infinite-Dimensional Systems. Birkhäuser Boston Inc., Boston (1995). [CrossRef] [Google Scholar]
  6. J.L. Lions, Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev. 30 (1988) 1–68. [Google Scholar]
  7. L. Tebou, A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations. ESAIM Control Optim. Calc. Var. 14 (2008) 561–574. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. X. Zhang, Explicit observability estimate for the wave equation with potential and its application. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 456 (2000) 1101–1115. [CrossRef] [MathSciNet] [Google Scholar]
  9. X. Zhang, A unified controllability/observability theory for some stochastic and deterministic partial differential equations. Proceedings of the International Congress of Mathematicians, Vol. IV. Hindustan Book Agency, New Delhi (2010) 3008–3034. [Google Scholar]
  10. E. Zuazua, Controllability and observability of partial differential equations: some results and open problems, in Handbook of Differential Equations: Evolutionary Equations, Vol. III. Handb. Differ. Equ. Elsevier/North-Holland, Amsterdam (2007) 527–621. [CrossRef] [Google Scholar]
  11. L. Hörmander, The Analysis of Linear Partial Differential Operators. IV. Fourier Integral Operators. Springer-Verlag, Berlin (2009). [Google Scholar]
  12. Y. Liu, Some sufficient conditions for the controllability of wave equations with variable coefficients. Acta Appl. Math. 128 (2013) 181–191. [CrossRef] [MathSciNet] [Google Scholar]
  13. T. Duyckaerts, X. Zhang and E. Zuazua, On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire. 25 (2008) 1–41. [CrossRef] [MathSciNet] [Google Scholar]
  14. V. Komornik and P. Loreti, Fourier Series in Control Theory. Springer-Verlag, New York (2005). [CrossRef] [Google Scholar]
  15. X. Fu, J. Yong and X. Zhang, Exact controllability for the multidimensional semilinear hyperbolic equations. SIAM J. Control Optim. 46 (2007) 1578–1614. [CrossRef] [MathSciNet] [Google Scholar]
  16. O. Yu. Imanuvilov, On Carlerman estimates for hyperbolic equations. Asymptot. Anal. 32 (2002) 185–220. [MathSciNet] [Google Scholar]
  17. V.K. Jena, Carleman estimate for ultrahyperbolic operators and improved interior control for wave equations. J. Diff. Equ. 302 (2021) 273–333. [CrossRef] [Google Scholar]
  18. A. Shao, On Carleman and observability estimates for wave equations on time dependent domains. Proc. Lond. Math. Soc. 67 (2019) 998–1064. [CrossRef] [MathSciNet] [Google Scholar]
  19. X. Fu and Z. Liao, Explicit observability inequality for the wave equation with variable coefficients. SIAM J. Control Optim. 60 (2022) 2344–2372. [CrossRef] [MathSciNet] [Google Scholar]
  20. X. Huang, O. Yu. Imanuvilov and M. Yamamoto, Stability for inverse source problems by Carleman estimates. Inverse Probl. 36 (2020) 125006. [CrossRef] [Google Scholar]
  21. M.V. Klibanov, Carleman estimate for global uniqueness, stablity and numerical metheds for coefficient inverse problems. J. Inverse Ill-Posed Probl. 21 (2013) 477–560. [CrossRef] [MathSciNet] [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.