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On some optimal control problems for the heat radiative transfer equation

Published online by Cambridge University Press:  15 August 2002

Sandro Manservisi  and
Knut Heusermann
Sandro Manservisi
Affiliation:
DIENCA - Universitá degli studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy; [email protected]. ITWM - Kaiserslautern University, Erwin-Schrdinger-Strasse, 67663 Kaiserslautern, Germany.
Knut Heusermann
Affiliation:
ITWM - Kaiserslautern University, Erwin-Schrdinger-Strasse, 67663 Kaiserslautern, Germany.
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Abstract

This paper is concerned with some optimal control problems for the Stefan-Boltzmann radiative transfer equation. The objective of the optimisation is to obtain a desired temperature profile on part of the domain by controlling the source or the shape of the domain. We present two problems with the same objective functional: an optimal control problem for the intensity and the position of the heat sources and an optimal shape design problem where the top surface is sought as control. The problems are analysed and first order necessity conditions in form of variation inequalities are obtained.

Keywords

Optimal controlheat radiative transferoptimal shape design.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 425 - 444
Copyright
© EDP Sciences, SMAI, 2000

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