no. 5
Some Controllability Results for the 2D Kolmogorov Equation
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1793-1815 
@article{AIHPC_2009__26_5_1793_0,
     author = {Beauchard, K. and Zuazua, E.},
     title = {Some {Controllability} {Results} for the {2D} {Kolmogorov} {Equation}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1793--1815},
     year = {2009},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     doi = {10.1016/j.anihpc.2008.12.005},
     mrnumber = {2566710},
     zbl = {1172.93005},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2008.12.005/}
}
TY  - JOUR
AU  - Beauchard, K.
AU  - Zuazua, E.
TI  - Some Controllability Results for the 2D Kolmogorov Equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 1793
EP  - 1815
VL  - 26
IS  - 5
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2008.12.005/
DO  - 10.1016/j.anihpc.2008.12.005
LA  - en
ID  - AIHPC_2009__26_5_1793_0
ER  - 
%0 Journal Article
%A Beauchard, K.
%A Zuazua, E.
%T Some Controllability Results for the 2D Kolmogorov Equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1793-1815
%V 26
%N 5
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2008.12.005/
%R 10.1016/j.anihpc.2008.12.005
%G en
%F AIHPC_2009__26_5_1793_0
Beauchard, K.; Zuazua, E. Some Controllability Results for the 2D Kolmogorov Equation. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1793-1815. doi: 10.1016/j.anihpc.2008.12.005

[1] Cabanillas V., De Menezes S., Zuazua E., Null Controllability in Unbounded Domains for the Semilinear Heat Equation With Nonlinearities Involving Gradient Terms, J. Optim. Theory Appl. 110 (2) (2001) 245-264. | Zbl | MR

[2] Coron J.-M., Control and Nonlinearity, Mathematical Surveys and Monographs, vol. 136, American Mathematical Society, 2007. | Zbl | MR

[3] Coron J.-M., Guerrero S., Singular Optimal Control: a Linear 1D Parabolic-Hyperbolic Example, Asymptotic Anal. 44 (3, 4) (2005) 237-257. | Zbl | MR

[4] Doubova A., Fernández-Cara E., González-Burgos M., Zuazua E., On the Controllability of Parabolic Systems With a Nonlinear Term Involving the State and the Gradient, SIAM J. Control Optim. 42 (3) (2002) 798-819. | Zbl | MR

[5] Duyckaerts T., Zhang X., Zuazua E., On the Optimality of the Observability Inequalities for Parabolic and Hyperbolic Systems With Potentials, Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008) 141. | MR | Numdam | EuDML | Zbl

[6] Fabre C., Puel J.-P., Zuazua E., Approximate Controllability of the Semilinear Heat Equation, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31-61. | Zbl | MR

[7] Fattorini H. O., Russell D., Exact Controllability Theorems for Linear Parabolic Equations in One Space Dimension, Arch. Ration. Mech. Anal. 43 (1971) 272-292. | Zbl | MR

[8] Fernández-Cara E., Zuazua E., Null and Approximate Controllability for Weakly Blowing Up Semilinear Heat Equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 583-616. | Zbl | MR | Numdam | EuDML

[9] Fernández-Cara E., Zuazua E., The Cost of Approximate Controllability for Heat Equations: the Linear Case, Adv. Differential Equations 5 (4-6) (2000) 465-514. | Zbl | MR

[10] Fernández-Cara E., Zuazua E., On the Null Controllability of the One-Dimensional Heat Equation With BV Coefficients, Comput. Appl. Math. 12 (2002) 167-190. | Zbl | MR

[11] Fursikov A., Imanuvilov O. Y., Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996. | Zbl | MR

[12] González-Burgos M., De Teresa L., Some Results on Controllability for Linear and Nonlinear Heat Equations in Unbounded Domains, Adv. Differential Equations 12 (11) (2007) 1201-1240. | Zbl | MR

[13] Hörmander L., Hypoelliptic Second Order Differential Equations, Acta Math. 119 (1967) 147-171. | Zbl | MR

[14] Imanuvilov O. Y., Boundary Controllability of Parabolic Equations, Uspekhi Mat. Nauk 48 (3(291)) (1993) 211-212. | MR

[15] Imanuvilov O. Y., Controllability of Parabolic Equations, Mat. Sb. 186 (6) (1995) 109-132. | Zbl | MR

[16] Imanuvilov O. Y., Yamamoto M., Carleman Estimate for a Parabolic Equation in Sobolev Spaces of Negative Order and Its Applications, in: Chen G., (Eds.), Control of Nonlinear Distributed Parameter Systems, Marcel Dekker, 2000, pp. 113-137. | Zbl | MR

[17] Lebeau G., Robbiano L., Contrôle Exact De L'équation De La Chaleur, Comm. Partial Differential Equations 20 (1995) 335-356. | Zbl | MR

[18] Lopez A., Zuazua E., Uniform Null Controllability for the One Dimensional Heat Equation With Rapidly Oscillating Periodic Density, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (5) (2002) 543-580. | Zbl | MR | Numdam

[19] Miller L., On the Null-Controllability of the Heat Equation in Unbounded Domains, Bull. Sci. Math. 129 (2) (2005) 175-185. | Zbl | MR

[20] Miller L., On Exponential Observability Estimates for the Heat Semigroup With Explicit Rates, Rendiconti Lincei: Matematica e Applicazioni 17 (4) (2006) 351-366. | Zbl | MR

[21] Martinez P., Vancostonoble J., Raymond J.-P., Regional Null Controllability of a Linearized Crocco Type Equation, SIAM J. Control Optim. 42 (2003) 709-728. | Zbl | MR

[22] Villani C., Hypocoercive Diffusion Operators, in: International Congress of Mathematicians, vol. III, Eur. Math. Soc., Zurich, 2006, pp. 473-498. | Zbl | MR

[23] Zuazua E., Approximate Controllability of the Semilinear Heat Equation: Boundary Control, in: Bristeau M. O., (Eds.), International Conference in Honour of Prof. R. Glowinski, Computational Sciences for the 21st Century, John Wiley and Sons, 1997, pp. 738-747. | Zbl

[24] Zuazua E., Finite Dimensional Null-Controllability of the Semilinear Heat Equation, J. Math. Pures Appl. 76 (1997) 237-264. | Zbl | MR

Cité par Sources :