Abstract
The article deals with the problem of optimal recovery of the solution of the wave equation at some time instant by known, but given with some error, functions determining the shape of the string at times t and T. The goal of the paper is to construct an optimal recovery method for the solution of the wave equation from inaccurate data. An important assumption used in the work is the possibility of representing the solution in the form of a Fourier series. The main solution method is the introduction of an auxiliary extremal problem for a conditional extremum, the solution of which determines the optimal recovery method. The result of the work is to find the optimal recovery method among all possible methods. The solution of the restoration problem and the value of the error of optimal recovery are obtained. Cases are indicated when it is possible to reduce the amount of initial information required for solving the problem.
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