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, p. 583-616
@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},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {5},
     year = {2000},
     pages = {583-616},
     zbl = {0970.93023},
     mrnumber = {1791879},
     language = {en},
     url = {http://www.numdam.org/item/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] Anita S., Barbu V., Internal null controllability of nonlinear heat equation, Preprint, 1999.

[2] Barbu V., Exact controllability of the superlinear heat equation, Preprint, 1998. | MR 1751309

[3] Brezis H., Cazenave Th., Martel Y., Ramiandrisoa A., Blow up for ut - Δu = g(u) revisited, Adv. Differential Equations 1 (1) (1996) 73-90. | MR 1357955 | Zbl 0855.35063

[4] Cannarsa P.M., Komornik V., Loreti P., Well posedness and control of the semilinear wave equation with iterated logarithms, ESAIM: COCV (to appear). | Numdam | MR 1680689 | Zbl 0939.35124

[5] Cazenave T., Haraux A., Equations d'évolution avec nonlinéarité logarithmique, Ann. Fac. Sci. Toulouse 2 (1980) 21-51. | Numdam | MR 583902 | Zbl 0411.35051

[6] Cazenave T., Haraux A., Barbu V., Introduction aux Problèmes d'Évolution Semilinéaires, Mathématiques & Applications, Ellipses, Paris, 1989. | Zbl 0786.35070

[7] Fabre C., Puel J.P., Zuazua E., Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh 125A (1995) 31-61. | MR 1318622 | Zbl 0818.93032

[8] Fernández-Cara E., Null controllability of the semilinear heat equation, ESAIM: COCV 2 (1997) 87-107. | Numdam | MR 1445385 | Zbl 0897.93011

[9] Fernández-Cara E., Zuazua E., The cost of approximate controllability for heat equations: The linear case, Adv. Differential Equations (to appear). | MR 1750109 | Zbl 1007.93034

[10] Fursikov A., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes, Vol. 34, Seoul National University, Korea, 1996. | MR 1406566 | Zbl 0862.49004

[11] Galaktionov V., On blow-up and degeneracy for the semilinear heat equation with source, Proc. Royal Soc. Edinburgh 115A (1990) 19-24. | MR 1059641 | Zbl 0715.35006

[12] Galaktionov V., Vázquez J.L., 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 1234014 | Zbl 0813.35033

[13] Glass O., Sur la contrôlabilité des fluides parfaits incompressibles, Ph.D. Thesis, Université de Paris XI, Orsay, France, January 2000.

[14] Henry J., 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] Imanuvilov O.Yu., Exact boundary controllability of the parabolic equation, Russian Math. Surveys 48 (1993) 211-212. | Zbl 0800.93172

[16] Khapalov A., 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 1350200 | Zbl 0846.35059

[17] Zuazua E., 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 1131832 | Zbl 0731.93011

[18] Zuazua E., Finite dimensional null-controllability of the semilinear heat equation, J. Math. Pures et Appl. 76 (1997) 237-264. | MR 1441986 | Zbl 0872.93014

[19] Zuazua E., Exact controllability for the semilinear wave equation in one space dimension, Ann. IHP, Analyse non Linéaire 10 (1996) 109-129. | Numdam | MR 1212631 | Zbl 0769.93017