Free Access
Volume 18, Number 1, January-March 2012
Page(s) 277 - 293
Published online 19 January 2011
  1. O.M. Aamo, A. Smyshlyaev and M. Krstić, Boundary control of the linearized Ginzburg-Landau model of vortex shedding. SIAM J. Control Optim. 43 (2005) 1953–1971. [Google Scholar]
  2. S.A. Avdonin and S.A. Ivanov, Families of exponentials. The method of moments in controllability problems for distributed parameter systems. Cambridge University Press (1995). [Google Scholar]
  3. J. Ball and M. Slemrod, Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems. Commun. Pure Appl. Math. XXXII (1979) 555–587. [Google Scholar]
  4. M. Bartuccelli, P. Constantin, C.R. Doering, J.D. Gibbon and M. Gisselfält, On the possibility of soft and hard turbulence in the complex Ginzburg Landau equation. Physica D 44 (1990) 421–444. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Baudouin and J.-P. Puel, Uniqueness and stability in an inverse problem for the Schrödinger equation. Inverse Probl. 18 (2002) 1537–1554. [Google Scholar]
  6. J.-M. Coron, Control and nonlinearity, Mathematical Surveys and Monographs 136. Am. Math. Soc., Providence (2007). [Google Scholar]
  7. J.-M. Coron and S. Guerrero, Singular optimal control : a linear 1-D parabolic-hyperbolic example. Asymptot. Anal. 44 (2005) 237–257. [MathSciNet] [Google Scholar]
  8. R.J. DiPerna, Convergence of approximate solutions to conservation laws. Arch. Ration. Mech. Anal. 82 (1983) 27–70. [CrossRef] [Google Scholar]
  9. X. Fu, A weighted identity for partial differential operators of second order and its applications. C. R. Acad. Sci. Paris, Sér. I 342 (2006) 579–584. [Google Scholar]
  10. X. Fu, Null controllability for the parabolic equation with a complex principal part. J. Funct. Anal. 257 (2009) 1333–1354. [CrossRef] [MathSciNet] [Google Scholar]
  11. A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations, Lect. Notes Ser. 34. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  12. O. Glass, A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit. J. Funct. Anal. 258 (2010) 852–868. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Ignat and E. Zuazua, Dispersive Properties of Numerical Schemes for Nonlinear Schrödinger Equations, in Foundations of Computational Mathematics, Santander 2005, London Math. Soc. Lect. Notes 331, L.M. Pardo, A. Pinkus, E. Suli and M.J. Todd Eds., Cambridge University Press (2006) 181–207. [Google Scholar]
  14. L. Ignat and E. Zuazua, Numerical dispersive schemes for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 47 (2009) 1366–1390. [CrossRef] [MathSciNet] [Google Scholar]
  15. A.E. Ingham, A note on Fourier transform. J. London Math. Soc. 9 (1934) 29–32. [CrossRef] [Google Scholar]
  16. A.E. Ingham, Some trigonometric inequalities with applications to the theory of series. Math. Zeits. 41 (1936) 367–379. [Google Scholar]
  17. J.P. Kahane, Pseudo-Périodicité et Séries de Fourier Lacunaires. Ann. Scient. Ec. Norm. Sup. 37 (1962) 93–95. [Google Scholar]
  18. V. Komornik and P. Loreti, Fourier Series in Control Theory. Springer-Verlag, New York (2005). [Google Scholar]
  19. M. Léautaud, Uniform controllability of scalar conservation laws in the vanishing viscosity limit. Preprint (2010). [Google Scholar]
  20. G. Lebeau, Contrôle de l’équation de Schrödinger. J. Math. Pures Appl. 71 (1992) 267–291. [Google Scholar]
  21. C.D. Levermore and M. Oliver, The complex Ginzburg Landau equation as a model problem, in Dynamical Systems and Probabilistic Methods in Partial Differential Equations, in Lect. Appl. Math. 31, Am. Math. Soc., Providence (1996) 141–190. [Google Scholar]
  22. A. López, X. Zhang and E. Zuazua, Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations. J. Math. Pures Appl. 79 (2000) 741–808. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Machtyngier, Exact controllability for the Schrödinger equation. SIAM J. Control Optim. 32 (1994) 24–34. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Mercado, A. Osses and L. Rosier, Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights. Inverse Probl. 24 (2008) 150–170. [Google Scholar]
  25. S. Micu and L. de Teresa, A spectral study of the boundary controllability of the linear 2-D wave equation in a rectangle. Asymptot. Anal. 66 (2010) 139–160. [Google Scholar]
  26. R.E.A.C. Paley and N. Wiener, Fourier Transforms in Complex Domains, AMS Colloq. Publ. 19. Am. Math. Soc., New York (1934). [Google Scholar]
  27. R.M. Redheffer, Completeness of sets of complex exponentials. Adv. Math. 24 (1977) 1–62. [CrossRef] [Google Scholar]
  28. L. Rosier and B.-Y. Zhang, Null controllability of the complex Ginzburg Landau equation. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 649–673. [Google Scholar]
  29. M. Salerno, B.A. Malomed and V.V. Konotop, Shock wave dynamics in a discrete nonlinear Schrödinger equation with internal losses. Phys. Rev. 62 (2000) 8651–8656. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser Advanced Texts, Springer, Basel (2009). [Google Scholar]
  31. R. Young, An Introduction to Nonharmonic Fourier Series. Academic Press, New York (1980). [Google Scholar]
  32. J. Zabczyk, Mathematical Control Theory : An Introduction. Birkhäuser, Basel (1992). [Google Scholar]
  33. X. Zhang, A remark on null exact controllability of the heat equation. SIAM J. Control Optim. 40 (2001) 39–53. [CrossRef] [MathSciNet] [Google Scholar]

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