Free access
Issue
ESAIM: COCV
Volume 17, Number 2, April-June 2011
Page(s) 506 - 551
DOI http://dx.doi.org/10.1051/cocv/2010017
Published online 23 April 2010
  1. V. Barbu, I. Lasiecka and R. Triggiani, Extended algebraic Riccati equations in the abstract hyperbolic case. Nonlinear Anal. 40 (2000) 105–129. [CrossRef] [MathSciNet]
  2. A. Bensoussan, G. Da. Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems, Systems & Control: Fondations & Applications 2. Boston, Birkhäuser (1993).
  3. J.-M. Buchot, Stabilization of the laminar turbulent transition location, in Proceedings MTNS 2000, El Jaï Ed. (2000).
  4. J.-M. Buchot, Stabilisation et contrôle optimal des équations de Prandtl. Ph.D. Thesis, École supérieure d'Aéronautique et de l'Espace, Toulouse (2002).
  5. J.-M. Buchot and J.-P. Raymond, A linearized model for boundary layer equations, in International Series of Numerical Mathematics 139, Birkhäuser (2001) 31–42.
  6. J.-M. Buchot and J.-P. Raymond, A linearized Crocco equation. J. Math. Fluid Mech. 8 (2006) 510–541. [CrossRef] [MathSciNet]
  7. J.-M. Buchot and J.-P. Raymond, Feedback stabilization of a boundary layer equation – Part 2: Nonhomogeneous state equation and numerical experiments. Appl. Math. Res. eXpress (2010) doi:10.1093/amrx/abp007.
  8. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique 4. Masson, Paris (1988).
  9. F. Flandoli, Algebric Riccati Equations arising in boundary control problems. SIAM J. Control Optim. 25 (1987) 612–636. [CrossRef] [MathSciNet]
  10. F. Flandoli, I. Lasiecka and R. Triggiani, Algebraic Riccati Equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems. Ann. Math. Pura Appl. 153 (1988) 307–382. [CrossRef]
  11. I. Lasiecka and R. Triggiani, Control theory for partial differential equations I, Abstract parabolic systems. Cambridge University Press, Cambridge (2000).
  12. I. Lasiecka and R. Triggiani, Optimal Control and Algebraic Riccati Equations under Singular Estimates for eAtB in the Abscence of Analycity, Part I: The stable case, in Lecture Notes in Pure in Applied Mathematics 225, Marcel Dekker (2002) 193–219.
  13. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes. Dunod, Paris (1968).
  14. O.A. Oleinik and V.N. Samokhin, Mathematical Models in Boundary Layer Theory, Applied Mathematics and Mathematical Computation 15. Chapman & Hall/CRC, Boca Raton, London, New York (1999).
  15. A.J. Pritchard and D. Salamon, The linear quadratic control of problem for infinite dimensional systems with unbounded input and output operators. SIAM J. Control Optim. 25 (1987) 121–144. [CrossRef] [MathSciNet]
  16. H. Triebel, Interpolation theory, Functions spaces, Differential operators. North Holland (1978).
  17. R. Triggiani, An optimal control problem with unbounded control operator and unbounded observation operator where Algebraic Riccati Equation is satisfied as a Lyapunov equation. Appl. Math. Letters 10 (1997) 95–102. [CrossRef]
  18. R. Triggiani, The Algebraic Riccati Equation with unbounded control operator: The abstract hyperbolic case revisited. Contemporary mathematics 209 (1997) 315–338.
  19. G. Weiss and H. Zwart, An example in LQ optimal control. Syst. Control Lett. 33 (1998) 339–349. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  20. Z. Xin and L. Zhang, On the global existence of solutions to the Prandtl's system. Adv. Math. 181 (2004) 88–133. [CrossRef] [MathSciNet]
  21. J. Zabczyck, Mathematical Control Theory. Birkhäuser (1995).