Abstract
A class of quasilinear variational data assimilation problems on the identification of the the initial-value functions is considered for the models governed by 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 optimality systems. The iterative algorithms for solving the problem are formulated and justified.
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