Speaker
Description
This talk deals with an optimal control problem, where the state variable is given as a parametrized balanced viscosity solution of a rate-independent system. Under certain assumptions on the data one can prove the existence of globally optimal solutions for external loads in H¹(0,T). Moreover, we investigate the approximability of optimal solutions by viscous regularized problems. However, the latter requires the existence of a continuous solution z̃ of the initial problem since the approximating sequence is not only constructed via viscous regularization but also with an additional penalty term depending on z̃ in the energy, which can be interpreted as a part of the external load ℓ. But the analysis is based on the fact that ℓ∈ H¹(0,T). Therefore, in order to weaken this assumption and allow for jumps of z̃ one has to deal with a more general definition, where external forces ℓ∈ BV(0,T) are included. However, already existing concepts are not suitable in this context of application so that we introduce a new solution concept.
