The problem of data assimilation for soil water movement

François-Xavier Le Dimet; Victor Petrovich Shutyaev; Jiafeng Wang; Mu Mu

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 3, page 331-345
  • ISSN: 1292-8119

Abstract

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The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.

How to cite

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Le Dimet, François-Xavier, et al. "The problem of data assimilation for soil water movement." ESAIM: Control, Optimisation and Calculus of Variations 10.3 (2010): 331-345. <http://eudml.org/doc/90733>.

@article{LeDimet2010,
abstract = { The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented. },
author = {Le Dimet, François-Xavier, Shutyaev, Victor Petrovich, Wang, Jiafeng, Mu, Mu},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Variational data assimilation; soil water movement; quasilinear parabolic problem; solvability; numerical analysis.; parabolic equation},
language = {eng},
month = {3},
number = {3},
pages = {331-345},
publisher = {EDP Sciences},
title = {The problem of data assimilation for soil water movement},
url = {http://eudml.org/doc/90733},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Le Dimet, François-Xavier
AU - Shutyaev, Victor Petrovich
AU - Wang, Jiafeng
AU - Mu, Mu
TI - The problem of data assimilation for soil water movement
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 3
SP - 331
EP - 345
AB - The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
LA - eng
KW - Variational data assimilation; soil water movement; quasilinear parabolic problem; solvability; numerical analysis.; parabolic equation
UR - http://eudml.org/doc/90733
ER -

References

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  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. Modelling8 (1986) 1-16.  Zbl0818.65056
  3. H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Zeitschrift183 (1983) 311-341.  Zbl0497.35049
  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.  
  6. J.C. Derber, Variational four-dimensional analysis using quasigeostrophic constraints. Mon. Wea. Rev.115 (1987) 998-1008.  
  7. J.-C. Gilbert and C. Lemarechal, Some numerical experiments with variable storage quasi-Newton algorithms. Math. Program.B25 (1989) 408-435.  Zbl0694.90086
  8. P.E. Gill, W. Murray and M.H. Wright, Practical Optimization. Academic Press (1981).  Zbl0503.90062
  9. D. Henry, Geometric Theory of Semilinear Parabolic Equations. New York, Springer (1981).  Zbl0456.35001
  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. Nauk41 (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.  Zbl0953.35019
  14. F.-X. Le Dimet, H.E. Ngodock and B. Luong, Sensitivity analysis in variational data assimilation. J. Met. Soc. Japan75 (1997) 245-255.  
  15. F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A38 (1986) 97-110.  
  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.  
  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).  Zbl0165.10801
  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).  Zbl0828.47053
  22. M. Mu, Global smooth solutions of two-dimensional Euler equations. Chin. Sci. Bull.35 (1990) 1895-1900.  Zbl0747.35033
  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.  
  24. O.A. Oleinik and E.V. Radkevich, Method of introducing a parameter for study of evolution equations. Uspehi Math. Nauk33 (1978) 7-76.  Zbl0449.35051
  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. Modelling10 (1995) 357-371.  Zbl0840.65040
  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 A44 (1992) 273-296.  

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