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Issue
ESAIM: COCV
Volume 16, Number 3, July-September 2010
Page(s) 794 - 805
DOI http://dx.doi.org/10.1051/cocv/2009014
Published online 02 July 2009
  1. A. Agrachev and M. Caponigro, Controllability on the group of diffeomorphisms. Preprint (2008).
  2. J.H. Albert, Genericity of simple eigenvalues for elliptic PDE's. Proc. Amer. Math. Soc. 48 (1975) 413–418. [CrossRef] [MathSciNet]
  3. W. Arendt and D. Daners, Uniform convergence for elliptic problems on varying domains. Math. Nachr. 280 (2007) 28–49. [CrossRef] [MathSciNet]
  4. V.I. Arnol'd, Modes and quasimodes. Funkcional. Anal. i Priložen. 6 (1972) 12–20.
  5. J.M. Ball, J.E. Marsden and M. Slemrod, Controllability for distributed bilinear systems. SIAM J. Control Optim. 20 (1982) 575–597. [CrossRef] [MathSciNet]
  6. K. Beauchard, Y. Chitour, D. Kateb and R. Long, Spectral controllability for 2D and 3D linear Schrödinger equations. J. Funct. Anal. 256 (2009) 3916–3976. [CrossRef] [MathSciNet]
  7. T. Chambrion, P. Mason, M. Sigalotti and U. Boscain, Controllability of the discrete-spectrum Schrödinger equation driven by an external field. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 329–349. [CrossRef] [MathSciNet]
  8. Y. Chitour, J.-M. Coron and M. Garavello, On conditions that prevent steady-state controllability of certain linear partial differential equations. Discrete Contin. Dyn. Syst. 14 (2006) 643–672. [CrossRef] [MathSciNet]
  9. S. Cox and E. Zuazua, The rate at which energy decays in a damped string. Comm. Partial Differential Equations 19 (1994) 213–243. [CrossRef] [MathSciNet]
  10. Y.C. de Verdière, Sur une hypothèse de transversalité d'Arnol'd. Comment. Math. Helv. 63 (1988) 184–193. [CrossRef] [MathSciNet]
  11. P. Hébrard and A. Henrot, Optimal shape and position of the actuators for the stabilization of a string. Systems Control Lett. 48 (2003) 199–209. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  12. P. Hébrard and A. Henrot, A spillover phenomenon in the optimal location of actuators. SIAM J. Control Optim. 44 (2005) 349–366 (electronic). [CrossRef] [MathSciNet]
  13. A. Henrot and M. Pierre, Variation et optimisation de formes, Mathématiques et Applications 48. Springer-Verlag, Berlin (2005).
  14. L. Hillairet and C. Judge, Generic spectral simplicity of polygons. Proc. Amer. Math. Soc. 137 (2009) 2139–2145. [CrossRef] [MathSciNet]
  15. T. Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften 132. Springer-Verlag New York, Inc., New York (1966).
  16. J.-L. Lions and E. Zuazua, Approximate controllability of a hydro-elastic coupled system. ESAIM: COCV 1 (1995/1996) 1–15 (electronic).
  17. J.-L. Lions and E. Zuazua, A generic uniqueness result for the Stokes system and its control theoretical consequences, in Partial differential equations and applications, Lect. Notes Pure Appl. Math. 177, Dekker, New York (1996) 221–235.
  18. T.J. Mahar and B.E. Willner, Sturm-Liouville eigenvalue problems in which the squares of the eigenfunctions are linearly dependent. Comm. Pure Appl. Math. 33 (1980) 567–578. [CrossRef] [MathSciNet]
  19. A.M. Micheletti, Metrica per famiglie di domini limitati e proprietà generiche degli autovalori. Ann. Scuola Norm. Sup. Pisa 26 (1972) 683–694. [MathSciNet]
  20. A.M. Micheletti, Perturbazione dello spettro dell'operatore di Laplace, in relazione ad una variazione del campo. Ann. Scuola Norm. Sup. Pisa. 26 (1972) 151–169.
  21. F. Murat and J. Simon, Étude de problèmes d'optimal design, Lecture Notes in Computer Sciences 41. Springer-Verlag, Berlin (1976).
  22. J.H. Ortega and E. Zuazua, Generic simplicity of the spectrum and stabilization for a plate equation. SIAM J. Control Optim. 39 (2000) 1585–1614 (electronic). [CrossRef] [MathSciNet]
  23. J.H. Ortega and E. Zuazua, Generic simplicity of the eigenvalues of the Stokes system in two space dimensions. Adv. Differential Equations 6 (2001) 987–1023. [MathSciNet]
  24. J.H. Ortega and E. Zuazua, Addendum to: Generic simplicity of the spectrum and stabilization for a plate equation [SIAM J. Control Optim. 39 (2000) 1585–1614; mr1825594]. SIAM J. Control Optim. 42 (2003) 1905–1910 (electronic).
  25. J. Sokołowski and J.-P. Zolésio, Introduction to shape optimization: Shape sensitivity analysis, Springer Series in Computational Mathematics 16. Springer-Verlag, Berlin (1992).
  26. E.D. Sontag, Mathematical control theory: Deterministic finite-dimensional systems, Texts in Applied Mathematics 6. Springer-Verlag, New York (1990).
  27. M. Teytel, How rare are multiple eigenvalues? Comm. Pure Appl. Math. 52 (1999) 917–934. [CrossRef] [MathSciNet]
  28. K. Uhlenbeck, Generic properties of eigenfunctions. Amer. J. Math. 98 (1976) 1059–1078. [CrossRef] [MathSciNet]
  29. E. Zuazua, Switching controls. J. Eur. Math. Soc. (to appear).