Null and approximate controllability for weakly blowing up semilinear heat equations

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1. [1] Anita S., Barbu V., Internal null controllability of nonlinear heat equation, Preprint, 1999. 
2. [2] Barbu V., Exact controllability of the superlinear heat equation, Preprint, 1998. MR1751309
3. [3] Brezis H., Cazenave Th., Martel Y., Ramiandrisoa A., Blow up for ut - Δu = g(u) revisited, Adv. Differential Equations1 (1) (1996) 73-90. Zbl0855.35063MR1357955
4. [4] Cannarsa P.M., Komornik V., Loreti P., Well posedness and control of the semilinear wave equation with iterated logarithms, ESAIM: COCV (to appear). Zbl0939.35124MR1680689
5. [5] Cazenave T., Haraux A., Equations d'évolution avec nonlinéarité logarithmique, Ann. Fac. Sci. Toulouse2 (1980) 21-51. Zbl0411.35051MR583902
6. [6] Cazenave T., Haraux A., Barbu V., Introduction aux Problèmes d'Évolution Semilinéaires, Mathématiques & Applications, Ellipses, Paris, 1989. Zbl0786.35070
7. [7] Fabre C., Puel J.P., Zuazua E., Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh125A (1995) 31-61. Zbl0818.93032MR1318622
8. [8] Fernández-Cara E., Null controllability of the semilinear heat equation, ESAIM: COCV2 (1997) 87-107. Zbl0897.93011MR1445385
9. [9] Fernández-Cara E., Zuazua E., The cost of approximate controllability for heat equations: The linear case, Adv. Differential Equations (to appear). Zbl1007.93034MR1750109
10. [10] Fursikov A., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes, Vol. 34, Seoul National University, Korea, 1996. Zbl0862.49004MR1406566
11. [11] Galaktionov V., On blow-up and degeneracy for the semilinear heat equation with source, Proc. Royal Soc. Edinburgh115A (1990) 19-24. Zbl0715.35006MR1059641
12. [12] Galaktionov V., Vázquez J.L., Regional blow-up in a semilinear heat equation with convergence to a Hamilton-Jacobi equation, SIAM J. Math. Anal24 (5) (1993) 1125-1276. Zbl0813.35033MR1234014
13. [13] Glass O., Sur la contrôlabilité des fluides parfaits incompressibles, Ph.D. Thesis, Université de Paris XI, Orsay, France, January 2000. 
14. [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. [15] Imanuvilov O.Yu., Exact boundary controllability of the parabolic equation, Russian Math. Surveys48 (1993) 211-212. Zbl0800.93172
16. [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. Zbl0846.35059MR1350200
17. [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. Zbl0731.93011MR1131832
18. [18] Zuazua E., Finite dimensional null-controllability of the semilinear heat equation, J. Math. Pures et Appl.76 (1997) 237-264. Zbl0872.93014MR1441986
19. [19] Zuazua E., Exact controllability for the semilinear wave equation in one space dimension, Ann. IHP, Analyse non Linéaire10 (1996) 109-129. Zbl0769.93017MR1212631

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