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On the solvability and numerical solution of data assimilation problems. (English) Zbl 0818.65056
Summary: The class of data assimilation problems for the equation of state, involving a nonlinear operator with a small parameter, is investigated. The conditions for the problem solvability are discussed and the analyticity of the solutions in relation to the small parameter is proved. These problems are shown to be equivalent, in a sense, to the ill-posed ones and regularization methods should be used for their solution. Some numerical algorithms are proposed and studied.

65K10 Numerical optimization and variational techniques
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L08 Numerical solution of ill-posed problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M15 Newton-type methods
34A34 Nonlinear ordinary differential equations and systems
86A05 Hydrology, hydrography, oceanography
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