AM  Vol.6 No.8 , July 2015
Asymptotic Behavior of a Bi-Dimensional Hybrid System
ABSTRACT
We study the asymptotic behavior of the solutions of a Hybrid System wrapping an elliptic operator.

Cite this paper
Gamboa, P. , Muñoz, J. , Vera, O. and Alves, M. (2015) Asymptotic Behavior of a Bi-Dimensional Hybrid System. Applied Mathematics, 6, 1228-1234. doi: 10.4236/am.2015.68115.
References
[1]   Banks, H.T., Fang, W., Silcox, R.J. and Smith, R.C. (1993) Aproximation Methods for Control of Acustic/Structures Models with Piezoceramic Actuators. Journal of Intelligent Material Systems and Structures, 4, 98-116.
http://dx.doi.org/10.1177/1045389X9300400113

[2]   Micu, S. and Zuazua, E. (1996) Stabilization and Periodic Solutions of a Hybrid System Arising in the Control of Noise. Proceedings of the IFIP TC7/WG-7.2 International Conference, Laredo, Lecture Notes in Pure and Applied Mathematics, Vol. 174, Marcel Dekker, New York, 219-230.

[3]   Micu, S. (1999) Periodic Solutions for a Bidimensional Hybrid System Arising in the Control of Noise. Advances in Differential Equations, 4, 529-560.

[4]   Cindea, N., Micu, S. and Pazoto, A.F. (2012) Periodic Solutions for a Weakly Dissipated Hybrid System. Journal of Mathematical Analysis and Applications, 385, 399-413.
http://dx.doi.org/10.1016/j.jmaa.2011.06.049

[5]   Hansen, S. and Zuazua, E. (1995) Exact Controllability and Stabilization of a Vibrating String with on Interior Point Mass. SIAM Journal on Control and Optimization, 33, 1357-1391.
http://dx.doi.org/10.1137/S0363012993248347

[6]   Littman, W. and Marcus, L. (1988) Exact Boundary Controllability of a Hybrid System of Elasticity. Archive for Rational Mechanics and Analysis, 103, 193-236.
http://dx.doi.org/10.1007/BF00251758

[7]   Micu, S.D. (1995) Analisis de un Sistema Hibrido Bidimensional Fluido-Estructura. Ph.D. Thesis, Universidad Complutense de Madrid, Madrid.

[8]   Avalos, G. and Lasiecka, I. (2003) Exact Controllability of Structural Acoustic Interactions. Journal de Mathématiques Pures et Appliquées, 82, 1047-1073.

[9]   Grisvard, P. (1985) Elliptic Problems in Non-Smooth Domains. Pitman.

[10]   Muñoz Rivera, J.E. (2007) Semigrupos e Equações Diferenciais Parciais. Textos Pós Graduação, LNCC.

[11]   Pazy, A. (1983) Semi-Groups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag.
http://dx.doi.org/10.1007/978-1-4612-5561-1

 
 
Top