Approximate Guaranteed Mean Square Estimates of Functionals on Solutions of Parabolic Problems with Fast Oscillating Coefficients Under Nonlinear Observations

The authors consider the problem of minimax estimation of a functional on the solution of parabolic problem with fast 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 estimate of the problem with averaged parameters is proved to be an approximate guaranteed mean square estimation of the original problem.