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Mathematics CAM Seminar – Speaker:  Pelin Guven Geredili

Author: las-digital | Image: las-digital

Postdoctoral Fellow, Dept of Mathematics, University of Nebraska – Lincoln

Title:  Stability Properties of Nondissipative Compressible Flow-Structure PDE Models

In this talk, we present recently derived results of uniform stability for a coupled partial differential equation
(PDE) system which models a compressible fluid-structure interaction of current interest within the
mathematical literature. The coupled PDE model under discussion will involve a linearized compressible,
viscous fluid flow evolving within a 3-D cavity, and a linear elastic plate–in the absence of rotational inertia—
which evolves on a portion of the fluid cavity wall. Since the fluid equation component is the result of a careful
linearization of the compressible Navier-Stokes equations about an arbitrary state, this interactive PDE
component will include a nontrivial ambient flow profile, which tends to complicate the analysis. Moreover,
there is an additional coupling PDE which determines the associated pressure variable of the fluid-structure
system. Under a suitable assumption on the ambient vector field, and by obtaining an appropriate estimate for
the associated fluid-structure generator on the imaginary axis, we provide a result of exponential stability for
finite energy solutions of the fluid-structure PDE system.