Ryabikova A. Evaluation of parameters of one-dimensional boundary value problems under incomplete data

In dissertation the minimax approach is developed to the evaluation problem of one-dimensional boundary value problems of general form under incomplete data for linear ordinary differential equations of the n-th-order and systems of such equations of the first order. It is obtained that minimax estimations of values of functionals from solutions which are observed and right-hand parts of equations which are included in formulation of boundary value problems are expressed via the solving of the systems of integro-differential equations of the special kind. The metod of minimax estimation of parameters of these boundary value problems, the solutions of which are definite up to the solutions of corresponding homogeneous problems and exist only if the right-hand parts of equations and boundary conditions which are included in formulation of initial boundary value problems are satisfied the certain compatibility conditions.