@article{AIHPC_2009__26_2_649_0, author = {Rosier, Lionel and Zhang, Bing-Yu}, title = {Null {Controllability} of the {Complex} {Ginzburg-Landau} {Equation}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {649--673}, publisher = {Elsevier}, volume = {26}, number = {2}, year = {2009}, doi = {10.1016/j.anihpc.2008.03.003}, mrnumber = {2504047}, zbl = {1170.35095}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.003/} }
TY - JOUR AU - Rosier, Lionel AU - Zhang, Bing-Yu TI - Null Controllability of the Complex Ginzburg-Landau Equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 649 EP - 673 VL - 26 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.003/ DO - 10.1016/j.anihpc.2008.03.003 LA - en ID - AIHPC_2009__26_2_649_0 ER -
%0 Journal Article %A Rosier, Lionel %A Zhang, Bing-Yu %T Null Controllability of the Complex Ginzburg-Landau Equation %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 649-673 %V 26 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.003/ %R 10.1016/j.anihpc.2008.03.003 %G en %F AIHPC_2009__26_2_649_0
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. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.003/
[1] Boundary Control of the Linearized Ginzburg-Landau Model of Vortex Shedding, SIAM J. Control Optim. 43 (6) (2005) 1953-1971, (electronic). | MR | Zbl
, , ,[2] Vector-Valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, vol. 96, Birkhäuser Verlag, Basel, 2001. | MR | Zbl
, , , ,[3] On the Possibility of Soft and Hard Turbulence in the Complex Ginzburg-Landau Equation, Physica D 44 (3) (1990) 421-444. | MR | Zbl
, , , , ,[4] J.L. Boldrini, E. Fernández-Cara, S. Guerrero, On the controllability of the Ginzburg-Landau equation, in preparation.
[5] An Initial-Boundary Value Problem for the Ginzburg-Landau Equation, Appl. Math. Lett. 5 (5) (1992) 31-34. | MR | Zbl
,[6] 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. | MR | Zbl
, ,[7] On the Controllability of the Heat Equation With Nonlinear Boundary Fourier Conditions, J. Differential Equations 196 (2) (2004) 385-417. | MR | Zbl
, , ,[8] Null Controllability of the Semilinear Heat Equation, ESAIM Control Optim. Calc. Var. 2 (1997) 87-103, (electronic). | Numdam | MR | Zbl
,[9] 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] Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996. | MR | Zbl
, ,[11] Dirichlet Inhomogeneous Boundary Value Problem for the Complex Ginzburg-Landau Equation, J. Differential Equations 198 (1) (2004) 176-195. | MR | Zbl
, ,[12] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. | MR | Zbl
,[13] 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. | MR | Zbl
,[14] 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. | MR | Zbl
, ,[15] Distribution-Valued Initial Data for the Complex Ginzburg-Landau Equation, Comm. Partial Differential Equations 22 (1-2) (1997) 39-48. | MR | Zbl
, ,[16] Inverse Problems for the Schrödinger Equation Via Carleman Inequalities With Degenerate Weights, Inverse Problems 24 (1) (2008), pp. 015017, 18. | MR | Zbl
, , ,[17] The Complex Ginzburg-Landau Equation on Large and Unbounded Domains: Sharper Bounds and Attractors, Nonlinearity 10 (1) (1997) 199-222. | MR | Zbl
,[18] Controllability of the Ginzburg-Landau Equation, C. R. Acad. Sci. Paris, Ser. I 346 (3-4) (2008) 167-172. | MR | Zbl
, ,[19] Global Existence Via Ginzburg-Landau Formalism and Pseudo-Orbits of Ginzburg-Landau Approximations, Commun. Math. Phys. 164 (1) (1994) 157-179. | MR | Zbl
,[20] Compact Sets in the Space , Ann. Mat. Pura Appl. (4) 146 (1987) 65-96. | MR | Zbl
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