抄録
In this work we examine the question of relaxability of infinite dimensional variational problems with state constraints. We consider systems governed by multivalued evolution equations (“trajectory problem”). We start with a new, general existence result for such inclusions with nonconvex valued orientor field. Then we prove a relaxation result. Next we introduce a cost functional, which we want to minimize over the trajectories, first of the original system and then over those of the relaxed one. Using perturbed and penalized versions of the original variational problem, we show that relaxability for the system is equivalent to a well-posedness notion that we call “strong calmness”. The same analysis is also carried on for semilinear systems. Now the hypotheses on the orientor field are weaker. We then show that the control problem is a special case of our trajectory problem. Finally we work an example of a distributed parameter control system.
