Free access
Issue
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
Page(s) 621 - 661
DOI http://dx.doi.org/10.1051/cocv:2002047
Published online 15 August 2002
  1. S. Anita and V. Barbu, Null controllability of nonlinear convective heat equation. ESAIM: COCV 5 (2000) 157-173. [CrossRef] [EDP Sciences]
  2. D.G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations. Arch. Rational Mech. Anal. 25 (1967) 81-122. [CrossRef] [MathSciNet]
  3. D.G. Aronson and J. Serrin, A maximum principle for nonlinear parabolic equations. Ann. Scuola Norm. Sup. Pisa 3 (1967) 291-305
  4. J.P. Aubin, L'analyse non linéaire et ses motivations économiques. Masson (1984).
  5. V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim. 42 (2000) 73-89. [CrossRef] [MathSciNet]
  6. T. Cazenave and A. Haraux, Introduction aux problèmes d'évolution semi-linéaires. Ellipses, Paris, Mathématiques & Applications (1990).
  7. S. Cox and E. Zuazua, The rate at which energy decays in a string damped at one end. Indiana Univ. Math. J. 44 (1995) 545-573. [MathSciNet]
  8. A. Doubova, E. Fernández-Cara, M. González-Burgos and E. Zuazua, On the controllability of parabolic system with a nonlinear term involving the state and the gradient. SIAM: SICON (to appear).
  9. C. Fabre, J.-P. Puel and E. Zuazua, (a) Approximate controllability for the semilinear heat equation. C. R. Acad. Sci. Paris Sér. I Math. 315 (1992) 807-812; (b) Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31-61.
  10. C. Fabre, J.-P. Puel and E. Zuazua, Approximate controllability for the linear heat equation with controls of minimal L norm. C. R. Acad. Sci. Paris Sér. I Math. 316 (1993) 679-684.
  11. E. Fernández-Cara, Null controllability of the semilinear heat equation. ESAIM: COCV 2 (1997) 87-107. [CrossRef] [EDP Sciences] [MathSciNet]
  12. E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations: The linear case. Adv. Differential Equations 5 (2000) 465-514. [MathSciNet]
  13. E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 583-616. [CrossRef] [MathSciNet]
  14. E. Fernández-Cara and E. Zuazua, On the null controllability of the one-dimensional heat equation with BV coefficients (to appear).
  15. A. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. Seoul National University, Korea, Lecture Notes 34 (1996).
  16. O.Yu. Imanuvilov, Controllability of parabolic equations. Mat. Sb. 186 (1995) 102-132.
  17. O.Yu. Imanuvilov and M. Yamamoto, Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications. Lecture Notes in Pure Appl. Math. 218 (2001) 113-137.
  18. O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uraltzeva, Linear and Quasilinear Equations of Parabolic Type. Nauka, Moskow (1967).
  19. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York (1983).
  20. D.L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Stud. Appl. Math. 52 (1973) 189-211.
  21. F.B. Weissler, Local existence and nonexistence for semilinear parabolic equations in Lp. Indiana Univ. Math. J. 29 (1980) 79-102. [CrossRef] [MathSciNet]
  22. F.B. Weissler, Semilinear evolution equations in Banach spaces. J. Funct. Anal. 32 (1979) 277-296. [CrossRef] [MathSciNet]
  23. E. Zuazua, Exact boundary controllability for the semilinear wave equation, in Nonlinear Partial Differential Equations and their Applications, Vol. X, edited by H. Brezis and J.-L. Lions. Pitman (1991) 357-391.
  24. E. Zuazua, Finite dimensional controllability for the semilinear heat equations. J. Math. Pures 76 (1997) 570-594.
  25. E. Zuazua, Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Control and Cybernetics 28 (1999) 665-683. [MathSciNet]