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.

Classification: 65K10

Keywords: variational data assimilation, quasilinear evolution problem, optimality system, control equation, solvability, iterative algorithms

@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}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, pages = {873-883}, doi = {10.1051/cocv:2002044}, zbl = {1070.65553}, mrnumber = {1932977}, language = {en}, url = {http://www.numdam.org/item/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, Volume 8 (2002) , pp. 873-883. doi : 10.1051/cocv:2002044. http://www.numdam.org/item/COCV_2002__8__873_0/

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