ON THE REDUCTION OF THE IDENTIFICATION OF THE PARAMETERS OF A DIFFERENTIAL EQUATION IN A HILBERT SPACE TO A BOUNDARY VALUE PROBLEM

The work considers the problem of differential equation parameter identification given in Hilbert space. Conditions of existence of problem solutions are established. They correspond to conditions of continuous dependence of solutions of differential equations on parameters. In case of linear model and space L-2 condition means convergence in mean quadratic sense on aprioric set. A constructive algorithm of identification problem solution in Hilbert space is developed. It is based on the considering of the estimation of differential equation solution and it results in the solving corresponding boundary value problem. The way of its reduction to initial value problems is offered. One partial case allowing problem solution not only in operator form is considered.