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A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.
@article{COCV_2002__8__873_0,
author = {Marchuk, Guri and Shutyaev, Victor},
title = {Solvability and numerical algorithms for a class of variational data assimilation problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {873--883},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002044},
mrnumber = {1932977},
zbl = {1070.65553},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002044/}
}
TY - JOUR AU - Marchuk, Guri AU - Shutyaev, Victor TI - Solvability and numerical algorithms for a class of variational data assimilation problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 873 EP - 883 VL - 8 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002044/ DO - 10.1051/cocv:2002044 LA - en ID - COCV_2002__8__873_0 ER -
%0 Journal Article %A Marchuk, Guri %A Shutyaev, Victor %T Solvability and numerical algorithms for a class of variational data assimilation problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 873-883 %V 8 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002044/ %R 10.1051/cocv:2002044 %G en %F COCV_2002__8__873_0
Marchuk, Guri; Shutyaev, Victor. Solvability and numerical algorithms for a class of variational data assimilation problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 873-883. doi: 10.1051/cocv:2002044
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