Optimal control of 3D state-constrained induction heating problems with nonlocal radiation effects
Please always quote using this URN: urn:nbn:de:0296-matheon-5811
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.
| Author: | Pierre-Etienne Druet, Olaf Klein, Jürgen Sprekels, Fredi Tröltzsch, Irwin Yousept |
|---|---|
| URN: | urn:nbn:de:0296-matheon-5811 |
| Referee: | Jürgen Sprekels |
| Language: | English |
| Date of first Publication: | 17.06.2009 |
| MSC-Classfication: | 35D10 |
| Tag: | Maxwell equations; State-constrained optimization; crystal growth; induction heating; nonlocal radiation boundary conditions |
| Institute: | Technische Universität Berlin |
| Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
| Project: | C9 Simulation and Optimization of Semiconductor Crystal Growth from the Melt Controlled by Traveling Magnetic Fields |
| MSC-Classification: | 35J60 Nonlinear elliptic equations |
| 49K20 Problems involving partial differential equations | |
| 78M50 Optimization | |
| 80M50 Optimization | |
| Preprint Number: | Matheon Preprint #579 |


