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ON THE EXPONENTIAL STABILITY FOR TWO MODELS TYPE
II CONGRESO NACIONAL DEL COLEGIO DE MATEMATICOS DEL PERU LAMBAYEQUE 2011 ON THE EXPONENTIAL STABILITY FOR TWO MODELS TYPE TIMOSHENKO YOLANDA SILVIA SANTIAGO AYALA 1 —————————————————— Using Semigroups Theory, regularity results and a Theorem associated to the Lumer Phillips Theorem, we prove the existence of solution for a Timoshenko beam model, in which two cases are considered: one and double damping. Also, using multiplicative techniques and the classic Gearthart theorem, introduced in Liu-Zheng [3], we prove that energy associated to the system decays exponentially to zero when t → +∞. Abstract. —————————————————— References [1] Feng, D-X, Shi, D-H, and Zhang, W. (1998). Boundary feedback stabilization of Timoshenko beam with boundary dissipation. Sci China Ser. A 41 No. 5: 483-490. [2] Kim, J.U. , Renardy, Y. (1987). Boundary control of the Timoshenko beam . SIAM J. Control Optim., 25 (6): 14171429. [3] Liu, Z. and Zheng, S. (1999). Semigroups associated with dissipative system, Chapman Hall / CRC. [4] Muñoz Rivera, J.E., Racke, R. (2007). Timoshenko systems with indefinite damping. Konstanzer Schriften Math. Inf. 230. [5] Santiago, Y. (2002). Global existence and exponential decay to the wave equation with localized frictional damping. PESQUIMAT Revista de la Fac. CC. MM. de la UNMSM. Vol V, No. 2: 1-19. [6] Santiago, Y. (2003). Sobre la analiticidad del semigrupo Co asociado a un sistema viscoelástico. PESQUIMAT Vol VI, No. 2: 27-36. [7] Santiago, Y. (2004). Estabilidad exponencial del Semigrupo C0 asociado a un sistema Termoelástico. PESQUIMAT Revista de la Fac. CC. MM. de la UNMSM. Vol VII , No. 1: 30-42. [8] Santiago, Y. (2005). Decaimiento exponencial de la solución débil de una ecuación de la Onda no lineal. PESQUIMAT Revista de la Fac. CC. MM. de la UNMSM. Vol VIII, No. 2: 29 - 43. [9] Santiago, Y. (2007). About decay of solution of the wave equation with dissipation. PROYECCIONES. Vol 26 No. 1: 37-71. [10] Santiago, Y. (2007). El lema de Nakao y algunas aplicaciones. PESQUIMAT. Vol X, No. 1 : 33-44. [11] Soufyane, A. and Wehbe, A. (2003). Exponential stability for the Timoshenko beam by a locally distributed damping. Electron. J. Differential Equations, 29 : 1-14. 1 Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas, Lima-Perú. E-mail address: [email protected] , [email protected]
