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All issues Volume 18 / No 3 (July-September 2012) ESAIM: COCV, 18 3 (2012) 712-747 References
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Issue
ESAIM: COCV
Volume 18, Number 3, July-September 2012
Page(s) 712 - 747
DOI https://doi.org/10.1051/cocv/2011168
Published online 21 October 2011
  1. S. Agmon, Lectures on Elliptic Boundary Values Problems. Van Nostrand (1965). [Google Scholar]
  2. S. Alinhac and P. Gérard, Opérateurs Pseudo-Différentiels et Théorème de Nash-Moser. Éditions du CNRS (1991). [Google Scholar]
  3. J.-P. Aubin and I. Ekeland, Applied Non Linear Analysis. John Wiley & Sons, New York (1984). [Google Scholar]
  4. V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim. 42 (2000) 73–89. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Bellassoued, Carleman estimates and distribution of resonances for the transparent obstacle and application to the stabilization. Asymptotic Anal. 35 (2003) 257–279. [MathSciNet] [Google Scholar]
  6. A. Benabdallah and M.G. Naso, Null controllability of a thermoelastic plate. Abstr. Appl. Anal. 7 (2002) 585–599. [CrossRef] [MathSciNet] [Google Scholar]
  7. A. Benabdallah, Y. Dermenjian and J. Le Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem. J. Math. Anal. Appl. 336 (2007) 865–887. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Benabdallah, Y. Dermenjian and J. Le Rousseau, On the controllability of linear parabolic equations with an arbitrary control location for stratified media. C. R. Acad. Sci. Paris, Ser. I 344 (2007) 357–362. [Google Scholar]
  9. M. Boulakia and A. Osses, Local null controllability of a two-dimensional fluid-structure interaction problem. ESAIM Control Optim. Calc. Var. 14 (2008) 1–42. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  10. H. Brezis, Analyse Fonctionnelle. Masson, Paris (1983). [Google Scholar]
  11. T. Carleman, Sur un problème d’unicité pour les systèmes d’équations aux dérivées partielles à deux variables indépendantes. Ark. Mat. Astr. Fys. 26B (1939) 1–9. [Google Scholar]
  12. L. de Teresa, Insensitizing controls for a semilinear heat equation. Comm. Partial Differential Equations 25 (2000) 39–72. [Google Scholar]
  13. M. Dimassi and J. Sjöstrand, Spectral Asymptotics in the Semi-classical Limit, London Mathematical Society Lecture Note Series 268. Cambridge University Press, Cambridge (1999). [Google Scholar]
  14. A. Doubova, E. Fernandez-Cara, M. Gonzales-Burgos and E. Zuazua, On the controllability of parabolic systems with a nonlinear term involving the state and the gradient. SIAM J. Control Optim. 41 (2002) 798–819. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Doubova, A. Osses and J.-P. Puel, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients. ESAIM : COCV 8 (2002) 621–661. [Google Scholar]
  16. E. Fernández-Cara and S. Guerrero, Global Carleman inequalities for parabolic systems and application to controllability. SIAM J. Control Optim. 45 (2006) 1395–1446. [CrossRef] [Google Scholar]
  17. E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations : the linear case. Adv. Differential Equations 5 (2000) 465–514. [MathSciNet] [Google Scholar]
  18. E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. Henri Poincaré, Analyse non linéaire 17 (2000) 583–616. [CrossRef] [MathSciNet] [Google Scholar]
  19. E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. 83 (2004) 1501–1542. [CrossRef] [MathSciNet] [Google Scholar]
  20. E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov and J.-P. Puel, Some controllability results for the N-dimensional Navier-Stokes and Boussinesq systems with N − 1 scalar controls. SIAM J. Control Optim. 45 (2006) 146–173. [CrossRef] [MathSciNet] [Google Scholar]
  21. C. Fabre and G. Lebeau, Prolongement unique des solutions de l’equation de Stokes. Comm. Partial Differential Equations 21 (1996) 573–596. [Google Scholar]
  22. A. Fursikov and O.Yu. Imanuvilov, Controllability of evolution equations, Lecture Notes 34. Seoul National University, Korea (1996). [Google Scholar]
  23. M. González-Burgos and R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force. Asymptotic Anal. 46 (2006) 123–162. [Google Scholar]
  24. A. Grigis and J. Sjöstrand, Microlocal Analysis for Differential Operators. Cambridge University Press, Cambridge (1994). [Google Scholar]
  25. L. Hörmander, Linear Partial Differential Operators. Springer-Verlag, Berlin (1963). [Google Scholar]
  26. L. Hörmander, The Analysis of Linear Partial Differential Operators IV. Springer-Verlag (1985). [Google Scholar]
  27. L. Hörmander, The Analysis of Linear Partial Differential Operators III. Springer-Verlag (1985). 2nd printing 1994. [Google Scholar]
  28. L. Hörmander, The Analysis of Linear Partial Differential Operators I. 2nd edition, Springer-Verlag (1990). [Google Scholar]
  29. O.Yu. Imanuvilov, Remarks on the exact controllability of Navier-Stokes equations. ESAIM : COCV 6 (2001) 39–72. [CrossRef] [EDP Sciences] [Google Scholar]
  30. O.Yu. Imanuvilov and T. Takahashi, Exact controllability of a fluid-rigid body system. J. Math. Pures Appl. 87 (2007) 408–437. [CrossRef] [MathSciNet] [Google Scholar]
  31. D. Jerison and G. Lebeau, Harmonic analysis and partial differential equations (Chicago, IL, 1996). chapter Nodal sets of sums of eigenfunctions, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago (1999) 223–239. [Google Scholar]
  32. F. Ammar Khodja, A. Benabdallah and C. Dupaix, Null controllability of some reaction-diffusion systems with one control force. J. Math. Anal. Appl. 320 (2006) 928–943. [CrossRef] [MathSciNet] [Google Scholar]
  33. F. Ammar Khodja, A. Benabdallah, C. Dupaix and I. Kostin, Null-controllability of some systems of parabolic type by one control force. ESAIM : COCV 11 (2005) 426–448. [Google Scholar]
  34. J. Le Rousseau, Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients. J. Differential Equations 233 (2007) 417–447. [CrossRef] [MathSciNet] [Google Scholar]
  35. J. Le Rousseau, and L. Robbiano, Carleman estimate for elliptic operators with coefficents with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations. Arch. Rational Mech. Anal. 105 (2010) 953–990. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Le Rousseau and L. Robbiano, Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces. Invent. Math. 183 (2011) 245–336. [Google Scholar]
  37. M. Léautaud, Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems. J. Funct. Anal. 258 (2010) 2739–2778. [CrossRef] [MathSciNet] [Google Scholar]
  38. G. Lebeau, Cours sur les inégalités de Carleman, Mastère Equations aux Dérivées Partielles et Applications. Faculté des Sciences de Tunis, Tunisie (2005). [Google Scholar]
  39. G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Comm. Partial Differential Equations 20 (1995) 335–356. [Google Scholar]
  40. G. Lebeau and L. Robbiano, Stabilisation de l’équation des ondes par le bord. Duke Math. J. 86 (1997) 465–491. [CrossRef] [MathSciNet] [Google Scholar]
  41. G. Lebeau and E. Zuazua, Null-controllability of a system of linear thermoelasticity. Arch. Rational Mech. Anal. 141 (1998) 297–329. [Google Scholar]
  42. A. Martinez, An Introduction to Semiclassical and Microlocal Analysis. Springer-Verlag (2002). [Google Scholar]
  43. S. Micu and E. Zuazua, On the lack of null-controllability of the heat equation on the half space. Port. Math. (N.S.) 58 (2001) 1–24. [MathSciNet] [Google Scholar]
  44. L. Miller, On the null-controllability of the heat equation in unbounded domains. Bull. Sci. Math. 129 (2005) 175–185. [CrossRef] [MathSciNet] [Google Scholar]
  45. L. Miller, On the controllability of anomalous diffusions generated by the fractional laplacian. Mathematics of Control, Signals, and Systems 3 (2006) 260–271. [Google Scholar]
  46. L. Miller, Unique continuation estimates for sums of semiclassical eigenfunctions and null-controllability from cones. Preprint (2008). http://hal.archives-ouvertes.fr/hal-00411840/fr. [Google Scholar]
  47. L. Miller, A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 1465–1485. [CrossRef] [MathSciNet] [Google Scholar]
  48. L. Robbiano, Théorème d’unicité adapté au contrôle des solutions des problèmes hyperboliques. Comm. Partial Differential Equations 16 (1991) 789–800. [Google Scholar]
  49. L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques. Asymptotic Anal. 10 (1995) 95–115. [MathSciNet] [Google Scholar]
  50. D. Robert, Autour de l’Approximation Semi-Classique, Progress in Mathematics 68. Birkhäuser Boston, Boston, MA (1987). [Google Scholar]
  51. J.-C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Differential Equations 66 (1987) 118–139. [CrossRef] [MathSciNet] [Google Scholar]
  52. M.A. Shubin, Pseudodifferential Operators and Spectral Theory. 2nd edition, Springer-Verlag, Berlin Heidelberg (2001). [Google Scholar]
  53. D. Tataru, Carleman estimates and unique continuation for the Schroedinger equation. Differential Integral Equations 8 (1995) 901–905. [MathSciNet] [Google Scholar]
  54. 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. [Google Scholar]
  55. M.E. Taylor, Pseudodifferential Operators. Princeton University Press, Princeton, New Jersey (1981). [Google Scholar]
  56. M.E. Taylor, Partial Differential Equations 2 : Qualitative Studies of Linear Equations, Applied Mathematical Sciences 116. Springer-Verlag, New-York (1996). [Google Scholar]
  57. G. Tenenbaum and M. Tucsnak, On the null-controllability of diffusion equations. preprint (2009). [Google Scholar]
  58. F. Trèves, Topological Vector Spaces, Distributions and Kernels. Academic Press, New York (1967). [Google Scholar]
  59. C. Zuily, Uniqueness and Non Uniqueness in the Cauchy Problem. Birkhäuser, Progress in mathematics (1983). [Google Scholar]

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