@article{COCV_1999__4__83_0,
author = {Khapalov, Alexander},
title = {Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {83--98},
year = {1999},
publisher = {EDP Sciences},
volume = {4},
mrnumber = {1680760},
zbl = {0926.93007},
language = {en},
url = {https://www.numdam.org/item/COCV_1999__4__83_0/}
}
TY - JOUR AU - Khapalov, Alexander TI - Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1999 SP - 83 EP - 98 VL - 4 PB - EDP Sciences UR - https://www.numdam.org/item/COCV_1999__4__83_0/ LA - en ID - COCV_1999__4__83_0 ER -
%0 Journal Article %A Khapalov, Alexander %T Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls %J ESAIM: Control, Optimisation and Calculus of Variations %D 1999 %P 83-98 %V 4 %I EDP Sciences %U https://www.numdam.org/item/COCV_1999__4__83_0/ %G en %F COCV_1999__4__83_0
Khapalov, Alexander. Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 83-98. https://www.numdam.org/item/COCV_1999__4__83_0/
[1] , Observation for the one-dimensional heat equation. Stadia Math. 48 ( 1973) 291-305. | Zbl | MR
[2] , Uniqueness result for Stokes equations and their consequences in linear and nonlinear problems. ESAIM: Control Optimization and Calculus of Variations 1 ( 1996) 267-302. | Zbl | MR | Numdam
[3] , and , Contrôlabilité approchée de l'équation de la chaleur semi-linéaire. C.R. Acad. Sci. Paris 315 ( 1992) 807-812. | Zbl | MR
[4] , and , Approximate controllability for the semilinear heat equation. Proc. Royal Soc. Edinburg 125A ( 1995) 31-61. | Zbl | MR
[5] and , Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations. Quarterly of Appl. Mathematics ( 1974) 45-69. | Zbl | MR
[6] and , Approximate controllability of the semilinear heat equation via optimal control. JOTA (to appear).
[7] and , Controllability and of evolution equations. Lect. Note Series 34, Res. Inst. Math., GARC, Seoul National University ( 1996). | Zbl | MR
[8] , On unique continuation of the solutions of the parabolic equation from a curve. Control and Cybernetics, Quarterly 25 ( 1996) 451-463. | Zbl | MR
[9] , 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. | Zbl | MR
[10] , and , Linear and quasi-linear equations of parabolic type. AMS, Providence, Rhode Island ( 1968).
[11] , Remarques sur la contrôlabilité approchée, in Proc. of "Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos", University of Málaga, Spain (October 1990). | Zbl | MR
[12] and , Entire functions and Müntz-Szász type approximation. Trans. AMS 157 ( 1971) 23-37. | Zbl | MR
[13] and , Observation and prediction for the heat equation. J. Math. Anal. Appl. 28 ( 1969) 303-312. | Zbl | MR
[14] , Global Solutions of Reaction-Diffusion Systems. Lecture Notes in Mathematics No. 1072 (Springer-Verlag, Berlin, 1984). | Zbl | MR
[15] , Controllability for partial differential equations of parabolic type. SIAM J. Cont. 12 ( 1974) 389-400. | Zbl | MR
[16] , The coefficient map for certain exponential sums. Neder. Akad. Wetemsch. Indag. Math. 48 ( 1986) 463-478. | Zbl | MR
[17] and , Unique continuation for some evolution equations. J. Diff. Equat. 66 ( 1987) 118-139. | Zbl | MR
[18] , Étude des sommes d'exponentielles réelles. Actualités Sci. Indust. No. 959 (Hermann, Paris, 1943). | Zbl | MR
[19] , A note on approximate controllability for semilinear one-dimensional heat equation. Appl. Math. Optim. 8 ( 1982) 275-285. | Zbl | MR
[20] , Finite dimensional null controllability for the semilinear heat equation. J. Math. Pures Appl. 76 ( 1997) 237-264. | Zbl | MR
[21] , Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Prep. del Depart, de Matematica Applicada, MA-UCM 1998-035, Universidad Complutense de Madrid ( 1998). | MR






