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Fluid structure interaction problem with changing thickness beam and slightly compressible fluid

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  • In this work, we consider the dynamical response of a non-linear beam with changing thickness, perturbed in both vertical and axial directions, interacting with a Darcy flow. We explore this fluid-structure interaction problem where the fluid is assumed to be slightly compressible. In an appropriate Sobolev norm, we build an energy functional for the displacement field of the beam and the gradient pressure of the fluid flow. We show that for a class of boundary conditions the energy functional is bounded by the flux of mass through the inlet boundary.
    Mathematics Subject Classification: Primary: 74F10, 35Q35; Secondary: 58C35.


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