Díaz Díaz, Jesús Ildefonso and Casal, Alfonso C. and Stich, Michael (2006) On some delayed nonlinear parabolic equations modeling CO oxidation. Dynamics of Continuous Discrete and Impulsive Systems: Series A - Mathematical Analysis, 13 (S). pp. 413-426. ISSN 1201-3390
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It is known that several features of many react ion-diffusion systems can be studied through an associated Complex Ginzburg-Landau Equation (CGLE). In particular, the study of the catalytic CO oxidation leads to the Krischer-Eiswirth-Ertl model, a nonlinear parabolic system, which can be controlled by a delayed feedback term. For the control of its uniform oscillations, we had already studied the corresponding delayed CGLE, developing first a pseudolinearization principle, of a very broad applicability, which led us to a range of parameters for the stability of those oscillations. In this work we first present some simulations which confirm the mentioned range of parameters, and gives other ranges for different behavior. Out of the setting of the CGLE, the dynamics is richer, so we present another method for the study of the existence, (monotonicity methods) and stability (with the pseudolinearization principle), directly for the mentioned parabolic system.
|Uncontrolled Keywords:||reaction-diffusion systems; feedback; chaos; pseudolinearization principle; nonlinear parabolic systems; delayed PDE's; Complex Ginzburg-Landau Equation; complexity; CO oxidation|
|Subjects:||Sciences > Physics > Mathematical physics|
H. Amann, Dynamic theory of quasilinear parabolic equations: II. Reaction-diffusion systems, Diff. Int. Equ.3 (1990), 13-75.
A. Ambrosetti, G. Prodi, A Primer of Nonlinear Analysis, Cambridge University Press, Cambridge, 1993.
Ph. Benilan, M.G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces. Book in preparation.
C. Beta, Controlling Chemical Turbulence in Surface Reactions, PhD thesis, Free University Berlin (2004)
C. Beta and A. S., Mikhailov, Controlling spatiotemporal chaos in oscillatory reaction diffusion systems by time-delay autosynchronization, Physica D, 199(2004), 173-184.
M. E. Bleich and J. E. S. Socolar, Controlling spatiotemporal dynamics with time-delay feedback, Phys. Rev. E, 54(1996) R17-R20.
A. C. Casal, J. I. Díaz, On the principle of pseudo-linearized stability: aplication to some delayed nonlinear parabolic equations. Proceedings of the 4th World Congress of Nonlinear Analysts (Orlando, FL, June 30- July 7, 2004). To be published as a special volume of Nonlinear Analysis, Theory, Methods and Applications.
A. C. Casal, J. I. Díaz, On the Pseudo-Linearization and Quasi-Linearization Principles, In CD-Rom Actas XIX CEDYA / IX CMA, Servicio de Publicaciones de la Univ. Carlos III, Madrid, 2005.
A. C. Casal, J. I. Díaz, J. F. Padial, 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.
H. Brezis, Opérateurs Maximaux Monotones, North Holland, Amsterdam, 1973.
G.,Ertl, Catalysis, Science and Technology, Vol. 4, edited by J. P. Anderson, Springer, Berlin, 1983.
M., Ipsen, L., Kramer, and P. B., Sörensen, Pysics Reports, 337(2000), 193-235.
K., Krischer, M., Eiswirth, and G., Ertl, Oscillatory CO oxidation on Pt(110): Modeling of temporal self-organization. J. Chem. Phys., 96(1992) 9161-9172.
C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum, New York, 1992.
K., Pyragas, Continuous control of chaos by self-contolling feedback, Phys. Lett. A, 170(1992), 421-426.
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988.
I.I. Vrabie, Compactness Methods for Nonlinear Evolutions, Second edition, Pitman Monographs, Longman, Essex, 1995.
|Deposited On:||24 May 2012 07:47|
|Last Modified:||06 Feb 2014 10:22|
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