# On some optimal control problems for the heat radiative transfer equation

Sandro Manservisi; Knut Heusermann

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 5, page 425-444
- ISSN: 1292-8119

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topManservisi, Sandro, and Heusermann, Knut. "On some optimal control problems for the heat radiative transfer equation." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 425-444. <http://eudml.org/doc/116571>.

@article{Manservisi2010,

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.
},

author = {Manservisi, Sandro, Heusermann, Knut},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; heat radiative transfer; optimal shape design.; optimal shape design; optimal control},

language = {eng},

month = {3},

pages = {425-444},

publisher = {EDP Sciences},

title = {On some optimal control problems for the heat radiative transfer equation},

url = {http://eudml.org/doc/116571},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Manservisi, Sandro

AU - Heusermann, Knut

TI - On some optimal control problems for the heat radiative transfer equation

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 5

SP - 425

EP - 444

AB -
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.

LA - eng

KW - Optimal control; heat radiative transfer; optimal shape design.; optimal shape design; optimal control

UR - http://eudml.org/doc/116571

ER -

## References

top- F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Computational Fluid Dynamics1 (1990) 303-326.
- R. Adams, Sobolev Spaces. Academic Press, New York (1975).
- V. Alekseev, V. Tikhomirov and S. Fomin, Optimal Control. Consultants Bureau, New York (1987).
- I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math.16 (1973) 179-192.
- D.M. Bedivan and G.J. Fix, An extension theorem for the space Hdiv. Appl. Math. Lett. (to appear).
- N. Di Cesare, O. Pironneau and E. Polak, Consistent approximations for an optimal design problem. Report 98005 Labotatoire d'analyse numérique, Paris, France (1998).
- P. Ciarlet, Introduction to Numerical Linear Algebra and Optimization. Cambridge University, Cambridge (1989).
- P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
- J.E. Dennis and R.B. Schnabel, Numerical methods for unconstrained optimisation and non-linear equations. Prentice-Hall Inc., New Jersey (1983).
- V. Girault and P. Raviart, The Finite Element Method for Navier-Stokes Equations: Theory and Algorithms. Springer-Verlag, New York (1986).
- M. Gunzburger and S. Manservisi, Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control. SIAM J. Numer. Anal. (to appear).
- M. Gunzburger and S. Manservisi, The velocity tracking problem for for Navier-Stokes flows with bounded distributed control. SIAM J. Control Optim. (to appear).
- J. Haslinger and P. Neittaanmäki, Finite Element Approximation for Optimal Shape Design. Wiley, Chichester (1988).
- K. Heusermann and S. Manservisi, Optimal design for heat radiative transfer systems. Comput. Methods Appl. Mech. Engrg. (to appear).
- F.P. Incropera and D.P. DeWitt, Fundamentals of Heat and Mass Transfer. Wiley, New York (1990).
- M. Modest, Radiative heat transfer. McGraw-Hill, New York (1993).
- O. Pironneau, Optimal shape design in fluid mechanics. Thesis, University of Paris (1976).
- O. Pironneau, On optimal design in fluid mechanics. J. Fluid. Mech.64 (1974) 97-110.
- O. Pironneau, Optimal shape design for elliptic systems. Springer, Berlin (1984).
- R.E. Showalter, Hilbert Space Methods for Partial Differential Equations. Electron. J. Differential Equations (1994) URIhttp://ejde.math.swt.edu/mono-toc.html
- J. Sokolowski and J. Zolesio, Introduction to shape optimisation: Shape sensitivity analysis. Springer, Berlin (1992).
- T. Tiihonen, Stefan-Boltzmann radiation on Non-convex Surfaces. Math. Methods Appl. Sci.20 (1997) 47-57.
- T. Tiihonen, Finite Element Approximations for a Heat Radiation Problem. Report 7/1995, Dept. of Mathematics, University of Jyväskylä (1995).
- V. Tikhomirov, Fundamental Principles of the Theory of Extremal Problems. Wiley, Chichester (1986).

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