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1'he inverse problem of identifying the memory kernel in the stress-strain-relation of Boltzmann type for a rod is reduced to an optimal control problem with a quadratic cost functional in the state for the related integrodifferential wave equation. For this problem necessary optimality conditions are derived and transformed into explicit form by means of suitably defined adjoint state functions.

On Optimality Conditions in some Control Problems for Memory Kernels in Viscoelasticity