On some optimal control problems for the heat radiative transfer equation
DIENCA - Universitá degli studi di Bologna, Via dei Colli 16, 40136
Bologna, Italy; email@example.com.
2 ITWM - Kaiserslautern University, Erwin-Schrdinger-Strasse, 67663 Kaiserslautern, Germany.
Revised: 2 June 2000
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.
Mathematics Subject Classification: 49N50 / 80A23
Key words: Optimal control / heat radiative transfer / optimal shape design.
© EDP Sciences, SMAI, 2000