Kovalyuk A. Minimax estimation of functionals from solutions to boundary-value problems under incomplete data

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0402U002158

Thesis Registration Form

0402U002158.pdf

Applicant for

Specialization

  • 01.05.04 - Системний аналіз і теорія оптимальних рішень

13-06-2002

Specialized Academic Board

Д 26.001.09

Taras Shevchenko National University of Kyiv

Essay

The thesis is devoted to the construction of minimax mean square estimates for functionals from solutions to boundary-value problems for elliptic partial differential equations of the second order and for systems of ordinary linear differential equations under observations depending on both of the solutions and of their derivatives. Problems of minimax estimation are reduced to certain optimal control problems of adjoint equations with quadratic performance criterions in the cases when the restrictions on unknown data of the problem are given completely or partly; in both cases we prove the theorems on a general form of minimax estimates of functionals from solutions of the cosidered equations and find the errors of estimation. It is established that these estimates are determined via the solutions of some systems of differential or integro-differential equations with partial or ordinary derivatives. We also prove that these equations are uniquely solvable.

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