| Abstract: |
| In this talk, preliminary stability results for two models are shared: (i) a transmission problem of an elastic-piezoelectric-elastic design with only one local damping acting on the longitudinal displacement of the center line of the piezoelectric material and (i) a transmission problem of a piezoelectric-elastic design with only one local damping acting on the elastic part. The problem (i) is shown to be exponentially stable whereas the stability of the problem (ii) strongly depends on the arithmetic nature of a quotient involving all the physical parameters of the system. Therefore, exponentially or polynomial stabilities can be obtained. In the case of the polynomial stability, the decay rate is provided in terms of a measure of irrationality of the quotient. Several open problems and future directions will be discussed. |
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