Free Access
Volume 10, Number 3, July 2004
Page(s) 331 - 345
Published online 15 June 2004
  1. V.I. Agoshkov and A.P. Mishneva, Calculation of the diffusion coefficient in a nonlinear parabolic equation. Preprint of the Department of Numerical Mathematics, USSR Acad. Sci., Moscow (1988), No. 200.
  2. V.I. Agoshkov and G.I. Marchuk, On the solvability and numerical solution of data assimilation problems. Russ. J. Numer. Anal. Math. Modelling 8 (1986) 1-16. [CrossRef]
  3. H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Zeitschrift 183 (1983) 311-341. [CrossRef] [MathSciNet]
  4. E. Blayo, J. Blum and J. Verron, Assimilation variationnelle de données en océanographie et réduction de la dimension de l'espace de contrôle. Équations aux Dérivées Partielles et Applications (Articles dédiées à Jacques-Louis Lions) (1998) 205-219.
  5. W.C. Chao and L.P. Chang, Development of a four-dimensional variational analysis system using the adjoint method at GLA. Part I: Dynamics. Mon. Wea. Rev. 120 (1992) 1661-1673. [CrossRef]
  6. J.C. Derber, Variational four-dimensional analysis using quasigeostrophic constraints. Mon. Wea. Rev. 115 (1987) 998-1008. [CrossRef]
  7. J.-C. Gilbert and C. Lemarechal, Some numerical experiments with variable storage quasi-Newton algorithms. Math. Program. B25 (1989) 408-435.
  8. P.E. Gill, W. Murray and M.H. Wright, Practical Optimization. Academic Press (1981).
  9. D. Henry, Geometric Theory of Semilinear Parabolic Equations. New York, Springer (1981).
  10. O.A. Ladyzhenskaya and N.N. Uraltseva, A survey on solvability of boundary value problems for uniformly elliptic and parabolic equations of the second order. Uspekhi Math. Nauk 41 (1986) 59-83.
  11. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and Quasilinear Parabolic Equations. Moscow, Nauka (1967).
  12. M.M. Lavrentiev, A priori Estimates and Existence Theorems for Nonlinear Parabolic Equations. Novosibirsk, Nauka (1982).
  13. F.-X. Le Dimet and I. Charpentier, Méthodes de second ordre en assimilation de données. Équations aux Dérivées Partielles et Applications (Articles dédiées à Jacques-Louis Lions) (1998) 623-639.
  14. F.-X. Le Dimet, H.E. Ngodock and B. Luong, Sensitivity analysis in variational data assimilation. J. Met. Soc. Japan 75 (1997) 245-255.
  15. F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38 (1986) 97-110. [CrossRef]
  16. Zh. Lei and Sh. Yang, The Dynamics of Soil Water. Tsinghua University Press (1986).
  17. Y. Li, I.M. Navon, W. Yang, X. Zou, J.R. Bates, S. Moorthi and R.W. Higgins, Four-dimensional variational data assimilation experiments with a multilevel semi-Lagrangian semi-implicit general circulation model. Mon. Wea. Rev. 122 (1994) 966-983. [CrossRef]
  18. J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. New York, Springer (1970).
  19. J.-L. Lions, Some Methods for Solving Nonlinear Problems. Moscow, Mir (1972).
  20. J.-L. Lions and E. Magenes, Problémes aux limites non homogènes et applications. Paris, Dunod (1968).
  21. G.I. Marchuk, V.I. Agoshkov and V.P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press Inc. New York (1996).
  22. M. Mu, Global smooth solutions of two-dimensional Euler equations. Chin. Sci. Bull. 35 (1990) 1895-1900.
  23. I.M. Navon, X. Zou, J. Derber and J. Sela, Variational data assimilation with an adiabatic version of the NMC spectral model. Mon. Wea. Rev. 120 (1992) 1433-1446. [CrossRef]
  24. O.A. Oleinik and E.V. Radkevich, Method of introducing a parameter for study of evolution equations. Uspehi Math. Nauk 33 (1978) 7-76.
  25. V. Penenko and N.N. Obraztsov, A variational initialization method for the fields of meteorological elements. Meteorol. Gidrol. 11 (1976) 1-11.
  26. V.P. Shutyaev, Some properties of the control operator in the problem of data assimilation and iterative algorithms. Russ. J. Numer. Anal. Math. Modelling 10 (1995) 357-371. [CrossRef]
  27. T.I. Zelenyak, M.M. Lavrentiev and M.P. Vishnevski, Qualitative Theory of Parabolic Equations. Utrecht, VSP Publishers (1997).
  28. T.I. Zelenyak and V.P. Michailov, Asymptotical behaviour of solutions of mathematical physics. Partial Diff. Eqs. (1970) 96-110.
  29. X. Zou, I. Navon and F.-X. Le Dimet, Incomplete observations and control of gravity waves in variational data assimilation. Tellus A 44 (1992) 273-296. [CrossRef]

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