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| The talk will focus on a system of Partial Differential Equations (PDE) which describes the interaction of a fluid flow in a
three-dimensional bounded domain, with the transversal displacement of a (fixed) part of its boundary. The mathematical model comprises a Stokes system for the fluid velocity field and a classical fourth order PDE for the elastic deformation of the plate; both the Euler-Bernoulli and the Kirchhoff models are specifically taken into consideration. The two distinct models give rise to two different stability results: namely, while uniform exponential stability holds true in the former case, rational decay rates of strong solutions have been established in the latter. An interesting feature of the obtained results is that the corresponding proofs are based on a frequency domain analysis rather than on energy/multiplier methods.
(The talk is based on joint work with George Avalos (University of Nebraska-Lincoln, USA)) |
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