In this paper, we study the existence of solutions for a cooperative elliptic system governed by Schrodingel' opel'atol' defined on R", then we discuss the optimal control of distributed type for this system.

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