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

Abstract

The 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 integro-differential wave equation. For this problem necessary optimality conditions are derived and transformed into explicit form by means of suitably defined adjoint state functions.