On some optimal control problems for the heat radiative transfer equation

 Access to full text

 Full (PDF)

1. [1] F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Computational Fluid Dynamics 1 ( 1990) 303-326. Zbl0708.76106
2. [2] R. Adams, Sobolev Spaces. Academic Press, New York ( 1975). Zbl0314.46030MR450957
3. [3] V. Alekseev, V. Tikhomirov and S. Fomin, Optimal Control. Consultants Bureau, New York ( 1987). Zbl0689.49001MR924574
4. [4] I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math. 16 ( 1973) 179-192. Zbl0258.65108MR359352
5. [5] D.M. Bedivan and G.J. Fix, An extension theorem for the space Hdiv. Appl. Math. Lett. (to appear). Zbl0915.46024
6. [6] N. Di Cesare, O. Pironneau and E. Polak, Consistent approximations for an optimal design problem. Report 98005 Labotatoire d'analyse numérique, Paris, France ( 1998). 
7. [7] P. Ciarlet, Introduction to Numerical Linear Algebra and Optimization. Cambridge University, Cambridge ( 1989). Zbl0672.65001MR1015713
8. [8] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam ( 1978). Zbl0383.65058MR520174
9. [9] J.E. Dennis and R.B. Schnabel, Numerical methods for unconstrained optimisation and non-linear equations. Prentice-Hall Inc., New Jersey ( 1983). Zbl0579.65058
10. [10] V. Girault and P. Raviart, The Finite Element Method for Navier-Stokes Equations: Theory and Algorithms. Springer-Verlag, New York ( 1986). Zbl0585.65077MR851383
11. [11] 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). Zbl0963.35150MR1759904
12. [12] M. Gunzburger and S. Manservisi, The velocity tracking problem for for Navier-Stokes flows with bounded distributed control. SIAM J. Control Optim. (to appear). Zbl0938.35118MR1720145
13. [13] J. Haslinger and P. Neittaanmäki, Finite Element Approximation for Optimal Shape Design. Wiley, Chichester ( 1988). Zbl0713.73062MR982710
14. [14] K. Heusermann and S. Manservisi, Optimal design for heat radiative transfer systems. Comput. Methods Appl. Mech. Engrg. (to appear). Zbl0952.49035
15. [15] F.P. Incropera and D.P. DeWitt, Fundamentals of Heat and Mass Transfer. Wiley, New York ( 1990). 
16. [16] M. Modest, Radiative heat transfer. McGraw-Hill, New York ( 1993). 
17. [17] O. Pironneau, Optimal shape design in fluid mechanics. Thesis, University of Paris ( 1976). 
18. [18] O. Pironneau, On optimal design in fluid mechanics. J. Fluid. Mech. 64 ( 1974) 97-110. Zbl0281.76020MR347229
19. [19] O. Pironneau, Optimal shape design for elliptic systems. Springer, Berlin ( 1984). Zbl0534.49001MR725856
20. [20] R.E. Showalter, Hilbert Space Methods for Partial Differential Equations. Electron. J. Differential Equations ( 1994) http://ejde.math.swt.edu/mono-toc.html Zbl0991.35001MR1302484
21. [21] J. Sokolowski and J. Zolesio, Introduction to shape optimisation: Shape sensitivity analysis. Springer, Berlin ( 1992). Zbl0761.73003
22. [22] T. Tiihonen, Stefan-Boltzmann radiation on Non-convex Surfaces. Math. Methods Appl. Sci. 20 ( 1997) 47-57. Zbl0872.35044MR1429330
23. [23] T. Tiihonen, Finite Element Approximations for a Beat Radiation Problem. Report 7/ 1995, Dept. of Mathematics, University of Jyväskylä ( 1995). 
24. [24] V. Tikhomirov, Fundamental Principles of the Theory of Extremal Problems. Wiley, Chichester ( 1986). Zbl0595.49001MR866483