Null controllability of the complex Ginzburg-Landau equation
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 2, page 649-673
- ISSN: 0294-1449
Access Full Article
topHow to cite
topRosier, Lionel, and Zhang, Bing-Yu. "Null controllability of the complex Ginzburg-Landau equation." Annales de l'I.H.P. Analyse non linéaire 26.2 (2009): 649-673. <http://eudml.org/doc/78859>.
@article{Rosier2009,
author = {Rosier, Lionel, Zhang, Bing-Yu},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ginzburg-Landau equation; null controllability; Calerman estimate},
language = {eng},
number = {2},
pages = {649-673},
publisher = {Elsevier},
title = {Null controllability of the complex Ginzburg-Landau equation},
url = {http://eudml.org/doc/78859},
volume = {26},
year = {2009},
}
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
PB - Elsevier
VL - 26
IS - 2
SP - 649
EP - 673
LA - eng
KW - Ginzburg-Landau equation; null controllability; Calerman estimate
UR - http://eudml.org/doc/78859
ER -
References
top- [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). Zbl1082.93016MR2177789
- [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. Zbl0978.34001MR1886588
- [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 D44 (3) (1990) 421-444. Zbl0702.76061MR1076337
- [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. Zbl0769.35049MR1345896
- [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. Zbl0915.65068MR1642557
- [7] Doubova A., Fernández-Cara E., González-Burgos M., On the controllability of the heat equation with nonlinear boundary Fourier conditions, J. Differential Equations196 (2) (2004) 385-417. Zbl1049.35042MR2028113
- [8] Fernández-Cara E., Null controllability of the semilinear heat equation, ESAIM Control Optim. Calc. Var.2 (1997) 87-103, (electronic). Zbl0897.93011MR1445385
- [9] Fu X., A weighted identity for partial differential operators of second order and its applications, C. R. Acad. Sci. Paris, Ser. I342 (8) (2006) 579-584. Zbl05045951MR2217919
- [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. Zbl0862.49004MR1406566
- [11] Gao H., Bu C., Dirichlet inhomogeneous boundary value problem for the complex Ginzburg–Landau equation, J. Differential Equations198 (1) (2004) 176-195. Zbl1058.35092MR2037754
- [12] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. Zbl0456.35001MR610244
- [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. Zbl1062.35004MR2108588
- [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. Zbl0845.35003MR1363028
- [15] Levermore C.D., Oliver M., Distribution-valued initial data for the complex Ginzburg–Landau equation, Comm. Partial Differential Equations22 (1–2) (1997) 39-48. Zbl0880.35110MR1434137
- [16] Mercado A., Osses A., Rosier L., Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights, Inverse Problems24 (1) (2008), pp. 015017, 18. Zbl1153.35407MR2384776
- [17] Mielke A., The complex Ginzburg–Landau equation on large and unbounded domains: sharper bounds and attractors, Nonlinearity10 (1) (1997) 199-222. Zbl0905.35043MR1430749
- [18] Rosier L., Zhang B.-Y., Controllability of the Ginzburg–Landau equation, C. R. Acad. Sci. Paris, Ser. I346 (3–4) (2008) 167-172. Zbl1134.35022MR2393635
- [19] Schneider G., Global existence via Ginzburg–Landau formalism and pseudo-orbits of Ginzburg–Landau approximations, Commun. Math. Phys.164 (1) (1994) 157-179. Zbl0803.35140MR1288157
- [20] Simon J., Compact sets in the space , Ann. Mat. Pura Appl. (4)146 (1987) 65-96. Zbl0629.46031MR916688
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.