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Abstract
We consider the quasi-static problem of viscoelastic body occupying a bounded region Ω ε R3 and subject to an elastic force on the boundary, with these restrictions are imposed on the form ofthe surface and on the boundary conditions, the solution of the problem obtained with the help of appropriate integral equations. We consider the boundary control of the viscoelastic body, and we flnd the necessary and sufficient conditions of optimal control for quasi-static problem.