no. 2
Null Controllability of the Complex Ginzburg-Landau Equation
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 649-673 
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     title = {Null {Controllability} of the {Complex} {Ginzburg-Landau} {Equation}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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}
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Rosier, Lionel; Zhang, Bing-Yu. Null Controllability of the Complex Ginzburg-Landau Equation. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 649-673. doi: 10.1016/j.anihpc.2008.03.003

[1] Aamo O. M., Smyshlyaev A., Krstić M., Boundary Control of the Linearized Ginzburg-Landau Model of Vortex Shedding, SIAM J. Control Optim. 43 (6) (2005) 1953-1971, (electronic). | Zbl | MR

[2] Arendt W., Batty C. J.K., Hieber M., Neubrander F., Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, vol. 96, Birkhäuser Verlag, Basel, 2001. | Zbl | MR

[3] Bartuccelli M., Constantin P., Doering C. R., Gibbon J. D., Gisselfält M., On the Possibility of Soft and Hard Turbulence in the Complex Ginzburg-Landau Equation, Physica D 44 (3) (1990) 421-444. | Zbl | MR

[4] J.L. Boldrini, E. Fernández-Cara, S. Guerrero, On the controllability of the Ginzburg-Landau equation, in preparation.

[5] Bu C., An Initial-Boundary Value Problem for the Ginzburg-Landau Equation, Appl. Math. Lett. 5 (5) (1992) 31-34. | Zbl | MR

[6] Chen Z., Hoffmann K.-H., Numerical Solutions of an Optimal Control Problem Governed by a Ginzburg-Landau Model in Superconductivity, Numer. Funct. Anal. Optim. 19 (7-8) (1998) 737-757. | Zbl | MR

[7] Doubova A., Fernández-Cara E., González-Burgos M., On the Controllability of the Heat Equation With Nonlinear Boundary Fourier Conditions, J. Differential Equations 196 (2) (2004) 385-417. | Zbl | MR

[8] Fernández-Cara E., Null Controllability of the Semilinear Heat Equation, ESAIM Control Optim. Calc. Var. 2 (1997) 87-103, (electronic). | Zbl | MR | Numdam

[9] Fu X., A Weighted Identity for Partial Differential Operators of Second Order and Its Applications, C. R. Acad. Sci. Paris, Ser. I 342 (8) (2006) 579-584. | MR

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

[11] Gao H., Bu C., Dirichlet Inhomogeneous Boundary Value Problem for the n+1 Complex Ginzburg-Landau Equation, J. Differential Equations 198 (1) (2004) 176-195. | Zbl | MR

[12] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. | Zbl | MR

[13] Hörmander L., The Analysis of Linear Partial Differential Operators. II, Differential Operators With Constant Coefficients, Classics in Mathematics, Springer-Verlag, Berlin, 2005, Reprint of the 1983 original. | Zbl | MR

[14] Levermore C. D., Oliver M., The Complex Ginzburg-Landau Equation as a Model Problem, in: Dynamical Systems and Probabilistic Methods in Partial Differential Equations, Berkeley, CA, 1994, Lectures in Appl. Math., vol. 31, Amer. Math. Soc., Providence, RI, 1996, pp. 141-190. | Zbl | MR

[15] Levermore C. D., Oliver M., Distribution-Valued Initial Data for the Complex Ginzburg-Landau Equation, Comm. Partial Differential Equations 22 (1-2) (1997) 39-48. | Zbl | MR

[16] Mercado A., Osses A., Rosier L., Inverse Problems for the Schrödinger Equation Via Carleman Inequalities With Degenerate Weights, Inverse Problems 24 (1) (2008), pp. 015017, 18. | Zbl | MR

[17] Mielke A., The Complex Ginzburg-Landau Equation on Large and Unbounded Domains: Sharper Bounds and Attractors, Nonlinearity 10 (1) (1997) 199-222. | Zbl | MR

[18] Rosier L., Zhang B.-Y., Controllability of the Ginzburg-Landau Equation, C. R. Acad. Sci. Paris, Ser. I 346 (3-4) (2008) 167-172. | Zbl | MR

[19] Schneider G., Global Existence Via Ginzburg-Landau Formalism and Pseudo-Orbits of Ginzburg-Landau Approximations, Commun. Math. Phys. 164 (1) (1994) 157-179. | Zbl | MR

[20] Simon J., Compact Sets in the Space L p (0,T;B), Ann. Mat. Pura Appl. (4) 146 (1987) 65-96. | Zbl | MR

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