Solution stability of a Timoshenko system with memory
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Abstract
This article studies the asymptotic behavior of dissipative systems with applications to beam modeling. Specifically, the existence, uniqueness and asymptotic behavior of a Timoshenko system with memory and with a Dirichlet type boundary condition are studied. The theory of semigroups is used to demonstrate the result of existence and uniqueness of solution and Gearhart theorem for the exponential stability of a Timoshenko system with total memory.
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References
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Raposo, C., Ferreira, J., Lima, M. & Castro, N. (2005). Exponential stability for the Timoshenko system with two weak dampings. Applied Mathematics Letters. 18(5), 530-536. DOI 10.1016/j.aml.2004.03.017.
Said-Hoauri, B. & Rahali, R. (2011). A stability result for a Timoshenko system with past history and a delay term in the internal feedback. Dynamic Systems and Applications. 20, 325-356. Disponible en: https://www.researchgate.net/publication/265179274_A_stability_result_for_a_Timoshenko_system_with_past_history_and_a_delay_term_in_the_internal_feedback.
Tarazona, V. (2018). Estudio de la estabilidad de un sistema de Timoshenko con historia pasada (o con memoria) [Tesis de Maestría]. Universidad Nacional Mayor de San Marcos. Disponible en: https://hdl.handle.net/20.500.12672/8435.
Liu, Z. & Zheng, S. (1999). Semigroups associated with dissipative systems. Chapman and Hall.
Ma, Z., Zhang, L., & Yang, X. (2011). Exponential stability for a Timoshenko type system with history. Journal of Mathematical Analitical Applied, 4(380), 295-309. DOI: 10.1016/j.jmaa.2011.02.078.
Raposo, C., Ferreira, J., Lima, M. & Castro, N. (2005). Exponential stability for the Timoshenko system with two weak dampings. Applied Mathematics Letters. 18(5), 530-536. DOI 10.1016/j.aml.2004.03.017.
Said-Hoauri, B. & Rahali, R. (2011). A stability result for a Timoshenko system with past history and a delay term in the internal feedback. Dynamic Systems and Applications. 20, 325-356. Disponible en: https://www.researchgate.net/publication/265179274_A_stability_result_for_a_Timoshenko_system_with_past_history_and_a_delay_term_in_the_internal_feedback.
Tarazona, V. (2018). Estudio de la estabilidad de un sistema de Timoshenko con historia pasada (o con memoria) [Tesis de Maestría]. Universidad Nacional Mayor de San Marcos. Disponible en: https://hdl.handle.net/20.500.12672/8435.