@article{AIHPC_2000__17_5_583_0, author = {Fern\'andez-Cara, Enrique and Zuazua, Enrique}, title = {Null and approximate controllability for weakly blowing up semilinear heat equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {583--616}, publisher = {Gauthier-Villars}, volume = {17}, number = {5}, year = {2000}, mrnumber = {1791879}, zbl = {0970.93023}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2000__17_5_583_0/} }
TY - JOUR AU - Fernández-Cara, Enrique AU - Zuazua, Enrique TI - Null and approximate controllability for weakly blowing up semilinear heat equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2000 SP - 583 EP - 616 VL - 17 IS - 5 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_2000__17_5_583_0/ LA - en ID - AIHPC_2000__17_5_583_0 ER -
%0 Journal Article %A Fernández-Cara, Enrique %A Zuazua, Enrique %T Null and approximate controllability for weakly blowing up semilinear heat equations %J Annales de l'I.H.P. Analyse non linéaire %D 2000 %P 583-616 %V 17 %N 5 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_2000__17_5_583_0/ %G en %F AIHPC_2000__17_5_583_0
Fernández-Cara, Enrique; Zuazua, Enrique. Null and approximate controllability for weakly blowing up semilinear heat equations. Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 5, pp. 583-616. http://www.numdam.org/item/AIHPC_2000__17_5_583_0/
[1] Internal null controllability of nonlinear heat equation, Preprint, 1999.
, ,[2] Exact controllability of the superlinear heat equation, Preprint, 1998. | MR
,[3] Blow up for ut - Δu = g(u) revisited, Adv. Differential Equations 1 (1) (1996) 73-90. | MR | Zbl
, , , ,[4] Well posedness and control of the semilinear wave equation with iterated logarithms, ESAIM: COCV (to appear). | Numdam | MR | Zbl
, , ,[5] Equations d'évolution avec nonlinéarité logarithmique, Ann. Fac. Sci. Toulouse 2 (1980) 21-51. | Numdam | MR | Zbl
, ,[6] Introduction aux Problèmes d'Évolution Semilinéaires, Mathématiques & Applications, Ellipses, Paris, 1989. | Zbl
, , ,[7] Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh 125A (1995) 31-61. | MR | Zbl
, , ,[8] Null controllability of the semilinear heat equation, ESAIM: COCV 2 (1997) 87-107. | Numdam | MR | Zbl
,[9] The cost of approximate controllability for heat equations: The linear case, Adv. Differential Equations (to appear). | MR | Zbl
, ,[10] Controllability of Evolution Equations, Lecture Notes, Vol. 34, Seoul National University, Korea, 1996. | MR | Zbl
, ,[11] On blow-up and degeneracy for the semilinear heat equation with source, Proc. Royal Soc. Edinburgh 115A (1990) 19-24. | MR | Zbl
,[12] Regional blow-up in a semilinear heat equation with convergence to a Hamilton-Jacobi equation, SIAM J. Math. Anal 24 (5) (1993) 1125-1276. | MR | Zbl
, ,[13] Sur la contrôlabilité des fluides parfaits incompressibles, Ph.D. Thesis, Université de Paris XI, Orsay, France, January 2000.
,[14] Contrôle d'un réacteur enzymatique à l'aide de modèles à paramètres distribués: Quelques problèmes de contrôlabilité de systèmes paraboliques, Ph.D. Thesis, Université Paris VI, 1978.
,[15] Exact boundary controllability of the parabolic equation, Russian Math. Surveys 48 (1993) 211-212. | Zbl
,[16] Some aspects of the asymptotic behavior of the solutions of the semilinear heat equation and approximate controllability, J. Math. Anal. Appl. 194 (1995) 858-882. | MR | Zbl
,[17] Exact boundary controllability for the semilinear wave equation, in: Brezis H., Lions J.L. (Eds.), Nonlinear Partial Differential Equations and their Applications, Vol. X, Pitman, 1991, pp. 357-391. | MR | Zbl
,[18] Finite dimensional null-controllability of the semilinear heat equation, J. Math. Pures et Appl. 76 (1997) 237-264. | MR | Zbl
,[19] Exact controllability for the semilinear wave equation in one space dimension, Ann. IHP, Analyse non Linéaire 10 (1996) 109-129. | Numdam | MR | Zbl
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