Abstract
We consider the Timoshenko beam system with two dynamic control boundary conditions of fractional derivative type. We show that the system is not uniformly stable by a spectrum method and we establish the polynomial stability using the semigroup theory of linear operators and a result obtained by Borichev and Tomilov.
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Benaissa, A., Benazzouz, S. Well-posedness and asymptotic behavior of Timoshenko beam system with dynamic boundary dissipative feedback of fractional derivative type. Z. Angew. Math. Phys. 68, 94 (2017). https://doi.org/10.1007/s00033-017-0836-2
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DOI: https://doi.org/10.1007/s00033-017-0836-2
Keywords
- Timoshenko beam system
- Dynamic boundary dissipation of fractional derivative type
- Polynomial stability