Free access
Issue
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
Page(s) 873 - 883
DOI http://dx.doi.org/10.1051/cocv:2002044
Published online 15 August 2002
  1. V.I. Agoshkov and G.I. Marchuk, On solvability and numerical solution of data assimilation problems. Russ. J. Numer. Analys. Math. Modelling 8 (1993) 1-16. [CrossRef]
  2. R. Bellman, Dynamic Programming. Princeton Univ. Press, New Jersey (1957).
  3. R. Glowinski and J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numerica 1 (1994) 269-378. [CrossRef]
  4. I.A. Krylov and F.L. Chernousko, On a successive approximation method for solving optimal control problems. Zh. Vychisl. Mat. Mat. Fiz. 2 (1962) 1132-1139 (in Russian).
  5. A.B. Kurzhanskii and A.Yu. Khapalov, An observation theory for distributed-parameter systems. J. Math. Syst. Estimat. Control 1 (1991) 389-440.
  6. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type. Nauka, Moscow (1967) (in Russian).
  7. F.X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus 38A (1986) 97-110. [CrossRef]
  8. J.-L. Lions, Contrôle Optimal des Systèmes Gouvernés par des Équations aux Dérivées Partielles. Dunod, Paris (1968).
  9. J.-L. Lions and E. Magenes, Problémes aux Limites non Homogènes et Applications. Dunod, Paris (1968).
  10. J.-L. Lions, On controllability of distributed system. Proc. Natl. Acad. Sci. USA 94 (1997) 4828-4835. [CrossRef]
  11. G.I. Marchuk, V.I. Agoshkov and V.P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press Inc., New York (1996).
  12. G.I. Marchuk and V.I. Lebedev, Numerical Methods in the Theory of Neutron Transport. Harwood Academic Publishers, New York (1986).
  13. G.I. Marchuk and V.V. Penenko, Application of optimization methods to the problem of mathematical simulation of atmospheric processes and environment, in Modelling and Optimization of Complex Systems, Proc. of the IFIP-TC7 Work. Conf. Springer, New York (1978) 240-252.
  14. G.I. Marchuk and V.P. Shutyaev, Iteration methods for solving a data assimilation problem. Russ. J. Numer. Anal. Math. Modelling 9 (1994) 265-279. [CrossRef]
  15. G. Marchuk, V. Shutyaev and V. Zalesny, Approaches to the solution of data assimilation problems, in Optimal Control and Partial Differential Equations. IOS Press, Amsterdam (2001) 489-497.
  16. G.I. Marchuk and V.B. Zalesny, A numerical technique for geophysical data assimilation problem using Pontryagin's principle and splitting-up method. Russ. J. Numer. Anal. Math. Modelling 8 (1993) 311-326. [CrossRef]
  17. E.I. Parmuzin and V.P. Shutyaev, Numerical analysis of iterative methods for solving evolution data assimilation problems. Russ. J. Numer. Anal. Math. Modelling 14 (1999) 265-274. [CrossRef]
  18. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mischenko, The Mathematical Theory of Optimal Processes. John Wiley, New York (1962).
  19. Y.K. Sasaki, Some basic formalisms in numerical variational analysis. Mon. Wea. Rev. 98 (1970) 857-883.
  20. V.P. Shutyaev, On a class of insensitive control problems. Control and Cybernetics 23 (1994) 257-266. [MathSciNet]
  21. V.P. Shutyaev, Some properties of the control operator in a data assimilation problem and algorithms for its solution. Differential Equations 31 (1995) 2035-2041. [MathSciNet]
  22. V.P. Shutyaev, On data assimilation in a scale of Hilbert spaces. Differential Equations 34 (1998) 383-389. [MathSciNet]
  23. A.N. Tikhonov, On the solution of ill-posed problems and the regularization method. Dokl. Akad. Nauk SSSR 151 (1963) 501-504. [MathSciNet]