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**:** 2016
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**:** . ., . . / . 61. .: , 2016. .88-94.

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** (.):** optimal control, nonstationary Sobolev type equations, relatively radial case.

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** (.):** In this paper we prove the existence of a unique optimal and hard control over solutions of ShowalterSidorov problem for the nonstationary model, which is described by Sobolev type equations. In this case, one of the operators in the equation is multiplied by a scalar function of the time-variable, besides stationary equation has a strong continuous degenerate resolving semigroup of operators.

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