Open Access
Volume 28, 2022
Article Number 14
Number of page(s) 26
Published online 24 February 2022
  1. V. Alexéev, S. Fomine and V. Tikhomirov, Commande optimale, Mir, Moscow (1982). [Google Scholar]
  2. F. Ammar-Kodjha, A. Benabdallah, M. González-Burgos and L. de Teresa, Recent results on the controllability of linear coupled parabolic problems: a survey. Math. Control Relat. Fields 1 (2011) 267–306. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Araruna, B.S.V. Araújo and E. Fernández-Cara, Stackelberg-Nash null controllability for some linear and semilinear degenerate parabolic equations. Math. Control Signals Syst. 30 (2018) Art. 14, 31 pp. [Google Scholar]
  4. F. Araruna, E. Fernández-Cara, S. Guerrero and M.C. Santos, New results on the Stackelberg-Nash exact control of linear parabolic equations. Systems Control Lett. 104 (2017) 78–85. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Araruna, E. Fernández-Cara and M.C. Santos, Stackelberg-Nash exact controllability for linear and semilinear parabolic equations. ESAIM: COCV 21 (2015) 835–856. [CrossRef] [EDP Sciences] [Google Scholar]
  6. F. Boyer, On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems, in CANUM 2012, Super-Besse, ESAIM Proc., EDP Sci., Les Ulis (2013). [Google Scholar]
  7. J.C. Cox and M. Rubinstein, Options Markets. Prentice-Hall, Englewood Cliffs, NJ (1985). [Google Scholar]
  8. J.I. Díaz, On the von Neumann problem and the approximate controllability of Stackelberg-Nash strategies for some environmental problems. Rev. R. Acad. Cien., Serie A. Math. 96 (2002) 343–356. [Google Scholar]
  9. J.I. Díaz and J.-L. Lions, On the approximate controllability of Stackelberg-Nash strategies. Ocean circulation and pollution control: a mathematical and numerical investigation (Madrid, 1997). Springer, Berlin (2004) 17–27. [CrossRef] [Google Scholar]
  10. E. Fernández-Cara and S. Guerrero, Global Carleman inequalities for parabolic systems and applications to controllability. SIAM J. Control Optim. 45 (2006) 1395–1446. [Google Scholar]
  11. A.V. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations, Lecture Note Series 34. Research Institute of Mathematics, Seoul National University, Seoul (1996). [Google Scholar]
  12. I.V. Girsanov, Lectures on mathematical theory of extremum problem, Lecture notes in Economics and mathematical systems 67. Springer-Verlag, Berlin (1972). [CrossRef] [Google Scholar]
  13. F. Guillén-González, F.P. Marques-Lopes and M.A. Rojas-Medar, On the approximate controllability of Stackelberg-Nash strategiesfor Stokes equations. Proc. Amer. Math. Soc. 141 (2013) 1759–1773. [Google Scholar]
  14. O.Yu. Imanuvilov, J.-P. Puel and M. Yamamoto, Carleman estimates for parabolic equations with nonhomogeneous boundary conditions. Chin. Ann. Math. Ser. B 30 (2009) 333–378. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.-L. Lions, Contrôle de Pareto de systèmes distribués. Le cas d’évolution. C.R. Acad. Sc. Paris, série I 302 (1986) 413–417. [Google Scholar]
  16. J.-L. Lions, Some remarks on Stackelberg’s optimization. Math. Models Methods Appl. Sci. 4 (1994) 477–487. [CrossRef] [Google Scholar]
  17. Y. Liu, T. Takahashi and M. Tucsnak, Single input controllability of a simplified fluid-structure interaction model. ESAIM: COCV 19 (2013) 20–42. [CrossRef] [EDP Sciences] [Google Scholar]
  18. V. Pareto, Cours d’économie politique. Rouge, Laussane, Switzerland (1896). [Google Scholar]
  19. A.M. Ramos, R. Glowinski and J. Periaux, Pointwise control of the Burgers equation and related Nash equilibria problems: A computational approach. J. Optim. Theory Appl. 112 (2001) 499–516. [Google Scholar]
  20. A.M. Ramos, R. Glowinski and J. Periaux, Nash equilibria for the multiobjective control of linear partial differential equations. J. Optim. Theory Appl. 112 (2002) 457–498. [CrossRef] [MathSciNet] [Google Scholar]
  21. S.M. Ross, An introduction to mathematical finance. Options and other topics. Cambridge University Press, Cambridge (1999). [Google Scholar]
  22. P. Wilmott, S. Howison, J. Dewynne, The mathematics of financial derivatives. Cambridge University Press, New York (1995). [CrossRef] [Google Scholar]

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