Publication: On the complex Ginzburg-Landau equation with a delayed feedback
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Publication Date
2006
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Casal, Alfonso C.
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World Scientific
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Abstract
We show how to stabilize the uniform oscillations of the complex Ginzburg-Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful study of the spectrum of the linearized operator.
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A. C. Casal, J. I. Díaz, J. F. Padial and L. Tello, On the stabilization of uniform oscillations for the complex Ginzburg-Landau equation by means of a global delayed mechanism, in CD-ROM Actas XVIII CEDYA/VIII CMA, Servicio de Publicaciones de la Univ. de Tarragona, 2003.
A. Aftalion and F. Pacella, Uniqueness and nondegeneracy for some nonlinear elliptic problems in a ball, preprint.
A. Aftalion and F. Pacella, Morse index and uniqueness for positive radial solutions of p-Laplace equations, preprint.
H. Amann, Dynamic theory of quasilinear parabolic equations: II. Reaction-diffusion systems, Diff. Int. Eqns. 3 (1990) 13–75.
A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis (Cambridge Univ. Press, 1993).
P. Auscher, L. Bathélemy, Ph. Bénilan and E. M. Ouhabaz, Absence de la L∞ -contractivité pour les semi-groupes associés aux opérateurs elliptiques complexes sous forme divergence, Potential Anal. 12 (2000) 169–189.
D. Battogtokh and A. Mikhailov, Controlling turbulence in the complex Ginzburg-Landau equation, Physica D 90 (1996) 84–95.
R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems (Elsevier, 1965).
Ph. Benilan, M. G. Crandall and A. Pazy, Nonlinear Evolution Equations in Banach Spaces, in preparation.
F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices (Birkhäuser, 1994).
R. Bermejo and J. A. Infante, A multigrid algorithm for the p-Laplacian, SIAM J. Scientific Computing 21 (2000) 1774–1789.
S. Carl and V. Lakshmikantham, Generalized quasilinearizarion and semilinear parabolic problems, Nonlinear Anal. 48 (2002) 947–960.
A. C. Casal and J. I. Díaz, On the principle of pseudo-linearized stability: Application to some delayed nonlinear parabolic equations, in Proc. of the 4th World Congress of Nonlinear Analysts (Orlando, FL, June 30-July 7, 2004).
A. C. Casal, J. I. Díaz, J. F. Padial and L. Tello, On the stabilization of uniform oscillations for the complex Ginzburg-Landau equation by means of a global delayed mechanism, in CD-ROM Actas XVIII CEDYA/VIII CMA, Univ. de Tarragona, 2003.
E. N. Chukwu, Differential Models and Neutral Systems for Controlling the Wealth of Nations (World Scientific, 2001).
H. Brezis, Opérateurs Maximaux Monotones (North-Holland, 1973).
J. I. Díaz and G. Hetzer, A functional quasilinear reaction-diffusion equation arising in climatology, in Équations aux Dérivées Partielles et Applications. Articles dédiés à J.-L. Lions (Elsevier, 1988), pp. 461–480.
J. I. Díaz, J. F. Padial, J. I. Tello and L. Tello, to appear.
J. K. Hale, Theory of Functional Differential Equations (Springer, 1977).
J. Hernández, F. Mancebo and J. M. Vega de Prada, On the linearization of some singular nonlinear elliptic problems and applications, Ann. I.H.P. Ann. Non Linear 19 (2002) 777–813.
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, 1984).
V. Lakshmikantham and S. Leela, Generalized Quasilinearization for Nonlinear Problems (Kluwer, 1995).
F. Mertens, R. Imbihl and A. Mikhailov, Turbulence and standing waves in oscillatory chemical reactions with global coupling, Chem. Phys. 101 (1994) 9903–9908.
M. E. Parrot, Linearized stability and irreducibility for a functional differential equation, SIAM J. Math. Anal. 23 (1992) 649–661.
K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A 170 (1992) 421–426.
W. M. Ruess, Linearized stability for nonlinear evolution equations, J. Evolution Eqns. 3 (2003) 361–373.
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Springer, 1988).
I. I. Vrabie, Compactness Methods for Nonlinear Evolutions, 2nd edn., Pitman Monographs (Longman, 1995).
J. Wu, Theory and Applications of Partial Functional Differential Equations (Springer, 1996).