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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.

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Metadaten
Author:Pierre-Etienne Druet, Olaf Klein, Jürgen Sprekels, Fredi Tröltzsch, Irwin Yousept
URN:urn:nbn:de:0296-matheon-5811
Referee:Jürgen Sprekels
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/06/17
Release Date:2009/06/16
Tag:
Institute:Technische Universität Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Mxx Basic methods / 78M50 Optimization
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Mxx Basic methods / 80M50 Optimization
Preprint Number:579
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