| Abstract: |
| The objective of this work is to study the well-posedness and stability questions for double wall carbon nanotubes modeled as linear one-dimensional coupled two Timoshenko beams in a bounded domain under frictional dampings. First, we prove the well-posedness of our system by applying the semigroups theory of linear operators. Second, we show several strong, non-exponential, exponential, polynomial and non-polynomial stability results depending on the number of frictional dampings, their position and some connections between the coefficients. In some cases, the optimality of the polynomial decay rate is also proved. The proofs of these stability results are based on a combination of the energy method and the frequency domain approach.
For the details, see the following paper: A. Guesmia, On the well-posedness and stability for carbon nanotubes as coupled two Timoshenko beams with frictional dampings, J. Appl. Anal. Comp., 14 (2024), 1-50. |
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