| Abstract: |
| In this talk, we consider a transmission problem for a string composed of three different types of materials: an elastic material (without dissipation), a thermoelastic material and a Kelvin-Voigt viscoelastic material. We discuss how the position of the different components plays an important role in the study of the stabilization. In particular, when considering three distinct components, as expected, when the viscoelastic component is not in the middle of the material, then there exists exponential stability of the solution. On the other hand, when the viscoelastic part is in the middle of the material, the exponential stability of the system achieved through the dissipation given by the heat conduction is destroyed by the local Kelvin-Voigt damping with a discontinuous coefficient at the interface. In this case, the solution decays polynomially as $t^{-2}$. |
|