TY - GEN A1 - Druet, Pierre-Etienne A1 - Klein, Olaf A1 - Sprekels, Jürgen A1 - Tröltzsch, Fredi A1 - Yousept, Irwin T1 - Optimal control of 3D state-constrained induction heating problems with nonlocal radiation effects N2 - The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditi! ons for an associated optimal control problem are established. KW - State-constrained optimization KW - Maxwell equations KW - nonlocal radiation boundary conditions KW - induction heating KW - crystal growth Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/581 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-5811 ER -