| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0289 |
| Timoshenko system with internal dissipation of fractional derivative type |
| Rafael Oliveira de Jesus,Carlos Alberto Raposo,Joilson Oliveira Ribeiro,Octavio Vera Villagran |
| Keywords:Timoshenko system, well-posedness, polynomial stability, fractional derivative type damping. |
| Abstract: |
| This manuscript deals with the well-posedness, strong, and polynomial stability of the Timoshenko system with internal dissipation of fractional derivative type. We use semigroup theory. The existence and uniqueness of the solution are obtained by applying the Lumer-Phillips Theorem. We present two results for the asymptotic behavior: strong stability of the C_0-semigroup associated with the system using the Arendt-Batty and Lyubich-V\~{u}"s general criterion and the polynomial stability applying the Borichev-Tomilov"s theorem. |
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