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Solvability and numerical algorithms for a class ofvariational dataassimilation problems

Published online by Cambridge University Press:  15 August 2002

Guri Marchuk  and
Victor Shutyaev
Guri Marchuk
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 GSP-1 Russia; shutyaev@inm.ras.ru.
Victor Shutyaev
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 GSP-1 Russia; shutyaev@inm.ras.ru.
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Abstract

A class of variationaldata assimilation problems on reconstructingthe initial-value functions is considered for the models governed byquasilinear evolution equations. The optimality system is reduced to theequation for the control function. The properties of the control equation are studied and thesolvability theorems are proved for linear and quasilinear data assimilationproblems. The iterative algorithms for solving the problem are formulated andjustified.

Keywords

Variational data assimilationquasilinear evolution problemoptimalitysystemcontrol equationsolvabilityiterative algorithms.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 873 - 883
Copyright
© EDP Sciences, SMAI, 2002

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