This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Aronna, M. SoledadBonnans, J. FrédéricKröner, Axel2022-06-302022-06-302020https://oa.tib.eu/renate/handle/123456789/9412https://doi.org/10.34657/8450In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions.eng510Optimal control of partial differential equationssemilinear parabolic equationsstate constraintssecond order analysiscontrol-affine problemsReport27 S.