Some controllability results for the 2D Kolmogorov equation
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 5, page 1793-1815
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBeauchard, K., and Zuazua, E.. "Some controllability results for the 2D Kolmogorov equation." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1793-1815. <http://eudml.org/doc/78913>.
@article{Beauchard2009,
author = {Beauchard, K., Zuazua, E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Kolmogorov equation; controllability; Carleman inequalities},
language = {eng},
number = {5},
pages = {1793-1815},
publisher = {Elsevier},
title = {Some controllability results for the 2D Kolmogorov equation},
url = {http://eudml.org/doc/78913},
volume = {26},
year = {2009},
}
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
PB - Elsevier
VL - 26
IS - 5
SP - 1793
EP - 1815
LA - eng
KW - Kolmogorov equation; controllability; Carleman inequalities
UR - http://eudml.org/doc/78913
ER -
References
top- [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. Zbl0997.93048MR1846267
- [2] Coron J.-M., Control and Nonlinearity, Mathematical Surveys and Monographs, vol. 136, American Mathematical Society, 2007. Zbl1140.93002MR2302744
- [3] Coron J.-M., Guerrero S., Singular optimal control: a linear 1D parabolic-hyperbolic example, Asymptotic Anal.44 (3, 4) (2005) 237-257. Zbl1078.93009MR2176274
- [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. Zbl1038.93041MR1939871
- [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 Linéaire25 (2008) 141. Zbl1248.93031MR2383077
- [6] Fabre C., Puel J.-P., Zuazua E., Approximate controllability of the semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A125 (1995) 31-61. Zbl0818.93032MR1318622
- [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. Zbl0231.93003MR335014
- [8] Fernández-Cara E., Zuazua E., Null and approximate controllability for weakly blowing up semilinear heat equations, Ann. Inst. H. Poincaré Anal. Non Linéaire17 (2000) 583-616. Zbl0970.93023MR1791879
- [9] Fernández-Cara E., Zuazua E., The cost of approximate controllability for heat equations: The linear case, Adv. Differential Equations5 (4–6) (2000) 465-514. Zbl1007.93034MR1750109
- [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. Zbl1119.93311MR2009951
- [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. Zbl0862.49004MR1406566
- [12] González-Burgos M., de Teresa L., Some results on controllability for linear and nonlinear heat equations in unbounded domains, Adv. Differential Equations12 (11) (2007) 1201-1240. Zbl1170.93007MR2372238
- [13] Hörmander L., Hypoelliptic second order differential equations, Acta Math.119 (1967) 147-171. Zbl0156.10701MR222474
- [14] Imanuvilov O.Y., Boundary controllability of parabolic equations, Uspekhi Mat. Nauk48 (3(291)) (1993) 211-212. MR1243631
- [15] Imanuvilov O.Y., Controllability of parabolic equations, Mat. Sb.186 (6) (1995) 109-132. Zbl0845.35040MR1349016
- [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. Zbl0977.93041MR1817179
- [17] Lebeau G., Robbiano L., Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations20 (1995) 335-356. Zbl0819.35071MR1312710
- [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 Linéaire19 (5) (2002) 543-580. Zbl1009.35009MR1922469
- [19] Miller L., On the null-controllability of the heat equation in unbounded domains, Bull. Sci. Math.129 (2) (2005) 175-185. Zbl1079.35018MR2123266
- [20] Miller L., On exponential observability estimates for the heat semigroup with explicit rates, Rendiconti Lincei: Matematica e Applicazioni17 (4) (2006) 351-366. Zbl1150.93006MR2287707
- [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. Zbl1037.93013MR1982289
- [22] Villani C., Hypocoercive diffusion operators, in: International Congress of Mathematicians, vol. III, Eur. Math. Soc., Zurich, 2006, pp. 473-498. Zbl1130.35027MR2275692
- [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. Zbl0916.93016
- [24] Zuazua E., Finite dimensional null-controllability of the semilinear heat equation, J. Math. Pures Appl.76 (1997) 237-264. Zbl0872.93014MR1441986
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.