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 (2004)
- Volume: 10, Issue: 3, page 331-345
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topDimet, François-Xavier Le, et al. "The problem of data assimilation for soil water movement." ESAIM: Control, Optimisation and Calculus of Variations 10.3 (2004): 331-345. <http://eudml.org/doc/244813>.
@article{Dimet2004,
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 = {Dimet, François-Xavier Le, 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},
number = {3},
pages = {331-345},
publisher = {EDP-Sciences},
title = {The problem of data assimilation for soil water movement},
url = {http://eudml.org/doc/244813},
volume = {10},
year = {2004},
}
TY - JOUR
AU - Dimet, François-Xavier Le
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
PY - 2004
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/244813
ER -
References
top- [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. MR1055578
- [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. Zbl0818.65056MR1211783
- [3] H.W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations. Math. Zeitschrift 183 (1983) 311-341. Zbl0497.35049MR706391
- [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 dédiés à Jacques-Louis Lions) (1998) 205-219. Zbl0915.35106
- [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. Zbl0694.90086MR1038242
- [8] P.E. Gill, W. Murray and M.H. Wright, Practical Optimization. Academic Press (1981). Zbl0503.90062MR634376
- [9] D. Henry, Geometric Theory of Semilinear Parabolic Equations. New York, Springer (1981). Zbl0456.35001MR610244
- [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. Zbl0639.35042MR878325
- [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 dédiés à Jacques-Louis Lions) (1998) 623-639. Zbl0953.35019MR1648245
- [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.
- [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). Zbl0203.09001MR271512
- [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). Zbl0828.47053MR1413046
- [22] M. Mu, Global smooth solutions of two-dimensional Euler equations. Chin. Sci. Bull. 35 (1990) 1895-1900. Zbl0747.35033MR1207458
- [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. Nauk 33 (1978) 7-76. Zbl0397.35033MR511881
- [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. Zbl0840.65040MR1356449
- [27] T.I. Zelenyak, M.M. Lavrentiev and M.P. Vishnevski, Qualitative Theory of Parabolic Equations. Utrecht, VSP Publishers (1997). Zbl0918.35001MR1644092
- [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.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.