Free Access
Issue
ESAIM: COCV
Volume 19, Number 2, April-June 2013
Page(s) 460 - 485
DOI https://doi.org/10.1051/cocv/2012017
Published online 15 February 2013
  1. N. Arada and J.P. Raymond, Dirichlet boundary control of semilinear parabolic equations, Part 1 : Problems with no state constraints. Appl. Math. Optim. 45 (2002) 125–143. [CrossRef] [MathSciNet] [Google Scholar]
  2. N. Arada and J.P. Raymond, Time optimal problems with Dirichlet boundary controls. Discrete Contin. Dyn. Syst. 9 (2003) 1549–1570. [CrossRef] [MathSciNet] [Google Scholar]
  3. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, Boston (1993). [Google Scholar]
  4. V. Barbu, The time optimal control of Navier-Stokes equations. Syst. Control Lett. 30 (1997) 93–100. [CrossRef] [MathSciNet] [Google Scholar]
  5. R.E. Bellman, I. Glicksberg and O.A. Gross, On the “bang-bang” control problem. Q. Appl. Math. 14 (1956) 11–18. [Google Scholar]
  6. C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. R. Soc. Edinburgh 125 (1995) 31–61. [CrossRef] [MathSciNet] [Google Scholar]
  7. H.O. Fattorini, Time optimal control of solutions of operational differential equations. SIAM J. Control 2 (1964) 54–59. [Google Scholar]
  8. H.O. Fattorini, Infinite Dimensional Linear Control Systems : The Time Optimal and Norm Optimal Problems. North-Holland Math. Stud. 201 (2005). [Google Scholar]
  9. H.O. Fattorini, Sufficiency of the maximum principle for time optimality. Cubo : A. Math. J. 7 (2005) 27–37. [Google Scholar]
  10. E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 17 (2000) 583–616. [CrossRef] [MathSciNet] [Google Scholar]
  11. A.V. Fursikov, Optimal Control of Distributed Systems, Theory and Applications. American Mathematical Society, Providence (2000). [Google Scholar]
  12. K. Kunisch and L.J. Wang, Time optimal controls of the linear Fitzhugh–Nagumo equation with pointwise control constraints. J. Math. Anal. Appl. (2012), doi: 10.1016/j.jmaa.2012.05.028. [Google Scholar]
  13. X.J. Li and J.M. Yong, Optimal Control Theory for Infinite Dimensional Systems. Birkhäuser, Boston (1995). [Google Scholar]
  14. J.L. Lions, Remarques sur la contrôlabilité approchée, in Jornadas Hispano-Francesas Sobre Control de Sistemas Distribuidos. University of Málaga, Spain (1991) 77–87. [Google Scholar]
  15. J.L. Lions, Remarks on approximate controllability. J. Anal. Math. 59 (1992) 103–116. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Micu and E. Zuazua, An introduction to the controllability of partial differential equations, in Quelques questions de théorie du contròle, edited by T. Sari. Collection Travaux en Cours Hermann (2004) 69–157. [Google Scholar]
  17. V.J. Mizel and T.I. Seidman, An abstract bang-bang principle and time optimal boundary control of the heat equation. SIAM J. Control Optim. 35 (1997) 1204–1216. [CrossRef] [MathSciNet] [Google Scholar]
  18. J.P. Raymond and H. Zidani, Pontryagin’s principle for time-optimal problems. J. Optim. Theory Appl. 101 (1999) 375–402. [CrossRef] [MathSciNet] [Google Scholar]
  19. E.J.P.G. Schmidt, The “bang-bang” principle for the time-optimal problem in boundary control of the heat equation. SIAM J. Control Optim. 18 (1980) 101–107. [CrossRef] [MathSciNet] [Google Scholar]
  20. G.S. Wang and L.J. Wang, The bang-bang principle of time optimal controls for the heat equation with internal controls. Syst. Control Lett. 56 (2007) 709–713. [CrossRef] [Google Scholar]
  21. L.J. Wang and G.S. Wang, The optimal time control of a phase-field system. SIAM J. Control Optim. 42 (2003) 1483–1508. [CrossRef] [MathSciNet] [Google Scholar]
  22. G.S. Wang and E. Zuazua, On the equivalence of minimal time and minimal norm controls for heat equations. SIAM J. Control Optim. 50 (2012) 2938–2958. [CrossRef] [MathSciNet] [Google Scholar]
  23. Z.Q. Wu, J.X. Yin and C.P. Wang, Elliptic and Parabolic Equations. World Scientific Publishing Corporation, New Jersey (2006). [Google Scholar]
  24. E. Zuazua, Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Control Cybern. 28 (1999) 665–683. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.