Issue
ESAIM: COCV
Volume 22, Number 4, October-December 2016
Special Issue in honor of Jean-Michel Coron for his 60th birthday
Page(s) 1097 - 1136
DOI https://doi.org/10.1051/cocv/2016046
Published online 05 August 2016
  1. C. Bardos, G. Lebeau and J. Rauch, Un exemple d’utilisation des notions de propagation pour le contrôle et la stabilisation de problèmes hyperboliques. Nonlinear hyperbolic equations in applied sciences. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue) (1989) 11–31. [Google Scholar]
  2. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Contr. Opt. 30 (1992) 1024–1065. [CrossRef] [Google Scholar]
  3. L. Baudouin, M. De Buhan and S. Ervedoza, Global Carleman estimates for waves and applications. Comm. Partial Differ. Eq. 38 (2013) 823–859. [Google Scholar]
  4. R. Bosi, Y. Kurylev and M. Lassas, Stability of the unique continuation for the wave operator via tataru inequality and applications. Preprint arXiv:1506.04318 (2015). [Google Scholar]
  5. N. Burq and P. Gérard, Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 749–752. [CrossRef] [MathSciNet] [Google Scholar]
  6. F. Chaves-Silva and G. Lebeau, Announcement (2015). [Google Scholar]
  7. J.-M. Coron and S. Guerrero, Singular optimal control: A linear 1-D parabolic-hyperbolic example. Asympt. Anal. 44 (2005) 237–257. [Google Scholar]
  8. J.-M. Coron, Control and nonlinearity. Vol. 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
  9. B. Dehman and S. Ervedoza, Dependence of high-frequency waves with respect to potentials. SIAM J. Control Optim. 52 (2014) 3722–3750. [CrossRef] [MathSciNet] [Google Scholar]
  10. B. Dehman and G. Lebeau, Analysis of the HUM control operator and exact controllability for semilinear waves in uniform time. SIAM J. Control Optim. 48 (2009) 521–550. [CrossRef] [MathSciNet] [Google Scholar]
  11. B. Dehman, J. Le Rousseau and M. Léautaud, Controllability of two coupled wave equations on a compact manifold. Arch. Ration. Mech. Anal. 211 (2014) 113–187. [CrossRef] [MathSciNet] [Google Scholar]
  12. S. Dolecki and D.L. Russell, A general theory of observation and control. SIAM J. Control Optim. 15 (1977) 185–220. [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. Henri Poincaré, Anal. Non Linéaire 25 (2008) 1–41. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Ervedoza and E. Zuazua, A systematic method for building smooth controls for smooth data. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 1375–1401. [Google Scholar]
  15. S. Gallot, D. Hulin and J. Lafontaine, Riemannian geometry. Universitext, 3rd edn. Springer-Verlag, Berlin (2004). [Google Scholar]
  16. P. Gérard, Microlocal defect measures. Comm. Partial Differ. Eq. 16 (1991) 1761–1794. [CrossRef] [Google Scholar]
  17. A. Haraux, T. Liard and Y. Privat, How to estimate observability constants of one-dimensional wave equations? propagation versus spectral methods. J. Evol. Equ. (2016) 1–32. [Google Scholar]
  18. L. Hörmander, The Analysis of Linear Partial Differential Operators, Volume III. Springer-Verlag (1985). Second printing (1994). [Google Scholar]
  19. L. Hörmander, A uniqueness theorem for second order hyperbolic differential equations. Commun. Partial Differ. Eq. 17 (1992) 699–714. [CrossRef] [Google Scholar]
  20. L. Hörmander, On the uniqueness of the Cauchy problem under partial analyticity assumptions. In Geometrical optics and related topics (Cortona, 1996). Vol. 32 of Progr. Nonlin. Differ. Eq. Appl. Birkhäuser Boston, Boston, MA (1997) 179–219. [Google Scholar]
  21. F. John, On linear partial differential equations with analytic coefficients. Unique continuation of data. Comm. Pure Appl. Math. 2 (1949) 209–253. [Google Scholar]
  22. V. Komornik, Exact controllability and stabilization. RAM: Res. Appl. Math. Masson, Paris (1994). The multiplier method. [Google Scholar]
  23. C. Laurent and M. Léautaud, Quantitative unique continuation for operators with partially analytic coefficients. Application to approximate control for waves. Preprint arXiv:1506.04254 (2015). [Google Scholar]
  24. G. Lebeau, Contrôle analytique. I. Estimations a priori. Duke Math. J. 68 (1992) 1–30. [CrossRef] [MathSciNet] [Google Scholar]
  25. G. Lebeau, Équation des ondes amorties. In Algebraic and geometric methods in mathematical physics (Kaciveli, 1993). Vol. 19 of Math. Phys. Stud. Kluwer Acad. Publ., Dordrecht (1996) 73–109. [Google Scholar]
  26. N. Lerner, Uniqueness for an ill-posed problem. J. Differ. Eq. 71 (1988) 255–260. [CrossRef] [Google Scholar]
  27. N. Lerner, Metrics on the phase space and non-selfadjoint pseudo-differential operators. Birkhäuser-Verlag, Basel (2010). [Google Scholar]
  28. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1, Vol. 8 of Recherches en Mathématiques Appliquées. Masson, Paris (1988). [Google Scholar]
  29. P. Lissy, A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation. C. R. Math. Acad. Sci. Paris 350 (2012) 591–595. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Lissy, Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport-diffusion equation. J. Differ. Eq. 259 (2015) 5331–5352. [Google Scholar]
  31. R.B. Melrose and J. Sjöstrand, Singularities of boundary value problems. I. Comm. Pure Appl. Math. 31 (1978) 593–617. [CrossRef] [MathSciNet] [Google Scholar]
  32. L. Miller, Escape function conditions for the observation, control, and stabilization of the wave equation. SIAM J. Control Optim. 41 (2002) 1554–1566. [CrossRef] [MathSciNet] [Google Scholar]
  33. L. Miller, Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time. J. Differ. Eq. 204 (2004) 202–226. [Google Scholar]
  34. L. Miller, How violent are fast controls for Schrödinger and plate vibrations? Arch. Ration. Mech. Anal. 172 (2004) 429–456. [Google Scholar]
  35. L. Miller, Controllability cost of conservative systems: resolvent condition and transmutation. J. Funct. Anal. 218 (2005) 425–444. [CrossRef] [MathSciNet] [Google Scholar]
  36. K.D. Phung, Waves, damped wave and observation. In Some problems on nonlinear hyperbolic equations and applications. Vol. 15 of Ser. Contemp. Appl. Math. CAM. Higher Ed. Press (2010) 386–412. [Google Scholar]
  37. J. Rauch and M. Taylor, Penetrations into shadow regions and unique continuation properties in hyperbolic mixed problems. Indiana Univ. Math. J. 22 (1972/73) 277–285. [CrossRef] [MathSciNet] [Google Scholar]
  38. J. Rauch and M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domains. Indiana Univ. Math. J. 24 (1974) 79–86. [CrossRef] [MathSciNet] [Google Scholar]
  39. L. Robbiano, Théorème d’unicité adapté au contrôle des solutions des problèmes hyperboliques. Commun. Partial Differ. Eq. 16 (1991) 789–800. [Google Scholar]
  40. L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques. Asymptotic Anal. 10 (1995) 95–115. [MathSciNet] [Google Scholar]
  41. J. Royer, Analyse haute fréquence de l’équation de Helmholtz dissipative. Thèse de Doctorat. Université de Nantes (2010). Available at http://www.math.sciences.univ-nantes.fr/˜jroyer/these.pdf. [Google Scholar]
  42. L. Robbiano and C. Zuily, Uniqueness in the Cauchy problem for operators with partially holomorphic coefficients. Invent. Math. 131 (1998) 493–539. [CrossRef] [MathSciNet] [Google Scholar]
  43. J. Royer, Limiting absorption principle for the dissipative Helmholtz equation. Commun. Partial Differ. Eq. 35 (2010) 1458–1489. [Google Scholar]
  44. R.T. Seeley, Complex powers of an elliptic operator. In Singular Integrals (Proc. of Sympos. Pure Math., Chicago, Ill., 1966). Amer. Math. Soc., Providence, R.I. (1967) 288–307. [Google Scholar]
  45. T.I. Seidman, How violent are fast controls? Math. Control Signals Systems 1 (1988) 89–95. [Google Scholar]
  46. M.A. Shubin, Pseudodifferential Operators and Spectral Theory, 2nd edn. Springer-Verlag, Berlin Heidelberg (2001). [Google Scholar]
  47. L. Tartar, H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 193–230. [CrossRef] [MathSciNet] [Google Scholar]
  48. D. Tataru, Unique continuation for solutions to PDE’s; between Hörmander’s theorem and Holmgren’s theorem. Commun. Partial Differ. Eq. 20 (1995) 855–884. [Google Scholar]
  49. D. Tataru, Carleman estimates, unique continuation and applications. Lecture notes. Available at https://math.berkeley.edu/˜tataru/papers/ucpnotes.ps (1999). [Google Scholar]
  50. D. Tataru, Unique continuation for operators with partially analytic coefficients. J. Math. Pures Appl. 78 (1999) 505–521. [CrossRef] [MathSciNet] [Google Scholar]
  51. M.E. Taylor, Reflection of singularities of solutions to systems of differential equations. Comm. Pure Appl. Math. 28 (1975) 457–478. [CrossRef] [MathSciNet] [Google Scholar]
  52. M.E. Taylor, Partial differential equations II. Qualitative studies of linear equations, Vol. 116 of Applied Mathematical Sciences, 2nd edn. Springer, New York (2011). [Google Scholar]
  53. E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. Inst. Henri Poincaré, Anal. Non Lin. 10 (1993) 109–129. [Google Scholar]

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