On some optimal control problems for the heat radiative transfer equation

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		425 - 444
DOI		10.1051/cocv:2000116

DOI: 10.1051/cocv:2000116

ESAIM: COCV, August 2000, Vol. 5, 425-444

On some optimal control problems for the heat radiative transfer equation

Sandro Manservisi
DIENCA - Universitá degli studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy; (sandro.manservisi@mail.ing.unibo.it)
ITWM - Kaiserslautern University, Erwin-Schr $\ddot{\rm o}$ dinger-Strasse, 67663 Kaiserslautern, Germany.

Knut Heusermann
ITWM - Kaiserslautern University, Erwin-Schr $\ddot{\rm o}$ dinger-Strasse, 67663 Kaiserslautern, Germany.

Received August 3, 1999. Revised June 2, 2000.

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 and phrases: Optimal control, heat radiative transfer, optimal shape design.

AMS Subject Classification: 49N50, 80A23

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