On the solvability and numerical solution of data assimilation problems.

*(English)*Zbl 0818.65056Summary: 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.

##### MSC:

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 |