A stability and numerical study of the solutions of a Timoshenko system with distributed delay |
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| Authors: | Carlos A Nonato Manoel J Dos Santos Jorge A J Avila Carlos A Raposo |
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| Institution: | 1. Department of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil;2. Faculty of Exact Sciences and Technology, Federal University of Pará, Abaetetuba, Pará, Brazil;3. Department of Mathematics, Federal University of São João del-Rei, São João del-Rei, Minas Gerais, Brazil |
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| Abstract: | In this work, we analyze the stability of the semigroup associated with a Timoshenko beam model with distributed delay in the rotation angle equation. We show that the type of stability resulting from the semigroup is directly related to some model coefficients, which constitute the velocities of the system's component equations. In the case of stability of the polynomial type, we prove that rate obtained is optimal. We conclude the work performing a numerical study of the solutions and their energies, associated to discrete system. |
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| Keywords: | distributed delay exponential decay finite differences optimal rate polynomial decay Timoshenko system |
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