Free access
Volume 6, 2001
Page(s) 467 - 488
Published online 15 August 2002
  1. R.A. Adams, Sobolev spaces. Academic Press, New-York (1975).
  2. H. Amann, Dual semigroups and second order linear elliptic boundary value problems. Israel J. Math. 45 (1983) 225-254. [CrossRef] [MathSciNet]
  3. S. Anita, Optimal control of parameter distributed systems with impulses. Appl. Math. Optim. 29 (1994) 93-107. [CrossRef] [MathSciNet]
  4. M. Berggren, R. Glowinski and J.L. Lions, A Computational Approach to Controllability Issues for Flow-Related Models, Part 1. Int. J. Comput. Fluid Dyn. 7 (1996) 237-252. [CrossRef]
  5. M. Berggren, R. Glowinski and J.L. Lions, A Computational Approach to Controllability Issues for Flow-Related Models, Part 2. Int. J. Comput. Fluid Dyn. 6 (1996) 253-247. [CrossRef]
  6. E. Casas, J.-P. Raymond and H. Zidani, Pontryagin's principle for local solutions of control problems with mixed control-state constraints. SIAM J. Control Optim. 39 (2000) 1182-1203. [CrossRef] [MathSciNet]
  7. E. Casas, M. Mateos and J.-P. Raymond, Pontryagin's principle for the control of parabolic equations with gradient state constraints. Nonlinear Anal. (to appear).
  8. E.J. Dean and P. Gubernatis, Pointwise Control of Burgers' Equation - A Numerical Approach. Comput. Math. Appl. 22 (1991) 93-100. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  9. Z. Ding, L. Ji and J. Zhou, Constrained LQR Problems in Elliptic distributed Control systems with Point observations. SIAM 34 (1996) 264-294.
  10. J. Droniou and J.-P. Raymond, Optimal pointwise control of semilinear parabolic equations. Nonlinear Anal. 39 (2000) 135-156. [CrossRef] [MathSciNet]
  11. J.W. He and R. Glowinski, Neumann control of unstable parabolic systems: Numerical approach. J. Optim. Theory Appl. 96 (1998) 1-55. [CrossRef] [MathSciNet]
  12. J.W. He, R. Glowinski, R. Metacalfe and J. Periaux, A numerical approach to the control and stabilization of advection-diffusion systems: Application to viscous drag reduction, Flow control and optimization. Int. J. Comput. Fluid Dyn. 11 (1998) 131-156. [CrossRef] [MathSciNet]
  13. H. Henrot and J. Sokolowski, Shape Optimization Problem for Heat Equation. Rapport de recherche INRIA (1997).
  14. D. Henry, Geometric Theory of Semilinear Parabolic Equations. Springer-Verlag, Berlin/Heidelberg/New-York (1981).
  15. K.-H. Hoffmann and J. Sokolowski, Interface optimization problems for parabolic equations. Control Cybernet. 23 (1994) 445-451. [MathSciNet]
  16. J.-P. Kernevez, The sentinel method and its application to environmental pollution problems. CRC Press, Boca Raton (1997).
  17. J.-L. Lions, Pointwise control for distributed systems, in Control and estimation in distributed parameters sytems, edited by H.T. Banks. SIAM, Philadelphia (1992) 1-39.
  18. O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type. AMS, Providence, RI, Transl. Math. Monographs 23 (1968).
  19. H.-C. Lee and O.Yu. Imanuvilov, Analysis of Neumann boundary optimal control problems for the stationary Boussinesq equations including solid media. SIAM J. Control Optim. 39 (2000) 457-477. [CrossRef] [MathSciNet]
  20. P.A. Nguyen, Optimal Control Localized on Thin Structure for Semilinear Parabolic Equations and the Boussinesq system. Thesis, Toulouse (2000).
  21. P.A. Nguyen and J.-P. Raymond, Control Localized On Thin Structure For Semilinear Parabolic Equations. Sém. Inst. H. Poincaré (to appear).
  22. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Berlin/Heidelberg/New-York (1983).
  23. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Tome 2, Fourier Analysis, Self-Adjointness. Academic Press, Inc. (1975).
  24. J.-P. Raymond and H. Zidani, Hamiltonian Pontryagin's principles for control problems governed by semilinear parabolic equations. Appl. Math. Optim. 39 (1999) 143-177. [CrossRef] [MathSciNet]
  25. J. Simon, Compact Sets in the Space Lp(0,T;B). Ann. Mat. Pura Appl. 196 (1987) 65-96.
  26. H. Triebel, Interpolation Theory, Functions Spaces, Differential Operators. North Holland Publishing Campany, Amsterdam/New-York/Oxford (1977).
  27. V. Vespri, Analytic Semigroups Generated in H-m,p by Elliptic Variational Operators and Applications to Linear Cauchy Problems, Semigroup theory and applications, edited by Clemens et al. Marcel Dekker, New-York (1989) 419-431.