| Abstract: |
| In this talk we consider a coupled system of nonlinear acoustic structure interactions. The model consists of the nonlinear Westervelt equation on a bounded domain with non homogeneous boundary conditions, coupled with a 4th order linear equation defined on a lower dimensional interface occupying part of the boundary of the domain, with transmission boundary conditions matching acoustic velocities and acoustic pressures.
While the well-posedness of the Westervelt model has been well studied in the literature, we here present new work on the analysis of this coupled problem. We establish local-in-time and global in time well-posedness for small data. Another contribution of this work, is a novel variational weak formulation of the linearized
system and a consideration of various boundary conditions.
If time permits, we will also provide an outlook on a control-shape optimization problem for this coupled system. |
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