| Abstract: |
| In this work we consider a multilayered wave-heat system where a 3-D wave equation is coupled with a 3-D heat equation via a 2-D interface whose dynamics is described by a 2-D wave equation. In particular, we undertake the problem of obtain explicit uniform rates of decay for smooth solutions of said FSI system; i.e., for solutions which correspond to initial data in the domain of the associated strongly continuous semigroup generator. To the best of our knowledge, this is the first such polynomial stability result obtained for multilayered FSI. By way of obtaining the rational decay result, we operated in the frequency domain and so dealt with a static FSI system: this static PDE system is essentially the image of the resolvent of the semigroup generator, as it acts on given finite energy data. |
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