Free Access
Volume 45, Number 2, March-April 2011
Page(s) 361 - 386
Published online 20 August 2010
  1. A. Belmiloudi and F. Brossier, A control method for assimilation of surface data in a linearized Navier-Stokes-type problem related to oceanography. SIAM J. Control Optim. 35 (1997) 2183–2197. [CrossRef] [MathSciNet] [Google Scholar]
  2. A.F. Bennett, Inverse Methods in Physical Oceanography. Cambridge University Press, Cambridge (1992). [Google Scholar]
  3. R. Bermejo and P. Galán del Sastre, Numerical studies of the long-term dynamics of the 2D Navier-Stokes equations applied to ocean circulation, in XVII CEDYA: Congress on Differential Equations and Applications, L. Ferragut and A. Santos Eds., Universidad de Salamanca, Salamanca (2001) 15–34. [Google Scholar]
  4. C. Bernardi, E. Godlewski and G. Raugel, A mixed method for time-dependent Navier-Stokes problem. IMA J. Numer. Anal. 7 (1987) 165–189. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Blayo, J. Blum and J. Verron, Assimilation variationnelle de données en océanographie et réduction de la dimension de l'espace de contrôle, in Équations aux dérivées partielles et applications, Articles dédiés à Jacques-Louis Lions, Gauthier-Villars, éd. Sci. Méd. Elsevier, Paris (1998) 199–219. [Google Scholar]
  6. J. Blum, B. Luong and J. Verron, Variational assimilation of altimeter data into a non-linear ocean model: Temporal strategies. ESAIM: Proc. 4 (1998) 21–57. [CrossRef] [EDP Sciences] [Google Scholar]
  7. C. Carthel, R. Glowinski and J.L. Lions, On exact and approximate boundary controllabilities for heat equation: a numerical approach. J. Optim. Theory Appl. 82 (1994) 429–484. [CrossRef] [MathSciNet] [Google Scholar]
  8. P. Courtier, O. Talagrand, Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory. Quart. J. Roy. Meteorol. Soc. 113 (1987) 1311–1328. [CrossRef] [Google Scholar]
  9. C. Fabre, J.-P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31–61. [Google Scholar]
  10. E. Fernández-Cara, S. Guerrero, O.Y. 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]
  11. E. Fernández-Cara, G.C. García and A. Osses, Controls insensitizing the observation of a quasi-geostrophic ocean model. SIAM J. Control Optim. 43 (2005) 1616–1639. [CrossRef] [MathSciNet] [Google Scholar]
  12. A.V. Fursikov and O.Y. Imanuilov, Local exact controllability of the two-dimensional Navier-Stokes equations. Matematicheskiĭ Sbornik 187 (1996) 103–138. [Google Scholar]
  13. A. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations. Lecture Notes, Research Institute of Mathematics, Seoul National University, Korea (1996). [Google Scholar]
  14. M. Ghil and P. Malanotte-Rizzoli, Data assimilation in meteorology and oceanography. Adv. Geophys. 33 (1991) 141–266. [Google Scholar]
  15. V. Girault and P.-A. Raviart, Finite Element Approximation of the Navier-Stokes Equations. Springer-Verlag, New York (1986). [Google Scholar]
  16. C. Hansen, Analysis of ill-posed problems by means of the L-curve. SIAM Rev. 34 (1992) 561–580. [CrossRef] [MathSciNet] [Google Scholar]
  17. F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations. Tellus 38A (1986) 97 –110. [CrossRef] [Google Scholar]
  18. J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin (1971). [Google Scholar]
  19. J.-L. Lions, Remarks on approximate controllability, Festschrift on the occasion of the 70th birthday of Samuel Agmon. J. Anal. Math. 59 (1992) 103–116. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.-L. Lions, Exact and approximate controllability for distributed parameter system, in VI Escuela de Otoño Hispano-Francesa sobre simulación numérica en física e ingeniería, Universidad de Sevilla, España (1994) 1–238. [Google Scholar]
  21. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications 1. Dunod (1968). [Google Scholar]
  22. B. Luong, J. Blum and J. Verron, A variational method for the resolution of a data assimilation problem in oceanography. Inv. Probl. 14 (1998) 979–997. [CrossRef] [Google Scholar]
  23. G.I. Marchuk, Formulation of theory of perturbations for complicated models. Appl. Math. Optim. 2 (1975) 1–33. [CrossRef] [MathSciNet] [Google Scholar]
  24. P.G. Myers and A.J. Weaver, A diagnostic barotropic finite-element ocean circulation model. J. Atmos. Ocean Tech. 12 (1995) 511–526. [CrossRef] [Google Scholar]
  25. A. Osses and J.-P. Puel, Boundary controllability of a stationary Stokes system with linear convection observed on an interior curve. J. Optim. Theory Appl. 99 (1998) 201–234. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Osses and J.-P. Puel, On the controllability of the Laplace equation observed on an interior curve. Rev. Mat. Complut. 11 (1998) 403–441. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.-P. Puel, Une approche non classique d'un problème d'assimilation de données. C. R. Math. Acad. Sci. Paris 335 (2002) 161–166. [CrossRef] [MathSciNet] [Google Scholar]
  28. J.-P. Puel, A nonstandard approach to a data assimilation problem and Tychonov regularization revisited. SIAM J. Control Optim. 48 (2009) 1089–1111. [CrossRef] [MathSciNet] [Google Scholar]
  29. L. Quartapelle, Numerical Solution of the Incompressible Navier-Stokes Equations. Birkhauser Verlag (1993). [Google Scholar]
  30. J. Verron, Altimeter data assimilation into ocean model: sensitivity to orbital parameters. J. Geophys. Res. 95 (1990) 11443–11459. [CrossRef] [Google Scholar]
  31. J. Verron, Nudging satellite altimeter data into quasi-geostrophic ocean models. J. Geophys. Res. 97 (1992) 7479–7492. [CrossRef] [Google Scholar]

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