UDC 517.9
3 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 g.chikrii@gmail.com
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APPROXIMATE GUARANTEED MEAN SQUARE ESTIMATES OF FUNCTIONALS
ON SOLUTIONS OF PARABOLIC PROBLEMS WITH FAST OSCILLATING
COEFFICIENTS UNDER NONLINEAR OBSERVATIONS
Abstract. The paper deals with the problem of minimax estimation of a functional on the solution of parabolic problem with rapidly oscillating coefficients. To solve this problem, the traditional minimax approach is used because of the presence of unknown functions on the right-hand side of the equation and in the initial condition. The existence of a guaranteed linear mean square estimate of the original problem is proved. An approximate solution of the original problem is found with the use of the averaging theory and the approximate synthesis methods for distributed systems. The main result of the work is to prove that the estimation of the problem with averaged parameters is an approximate guaranteed mean square estimation of the original problem.
Keywords: guaranteed mean-square estimates, parabolic equations, fast oscillating coefficients, observations, approximate estimates, superposition type operator.
FULL TEXT
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