Direct and inverse fluid-structure interaction problems (Q2719804)

The potential method is developed for three-dimensional fluid-structure interaction problems. Uniqueness and existence questions are investigated and the solvability of the direct problem is shown for arbitrary wave numbers and for arbitrary incident wave functions. The solutions are represented by potential-type integrals and their structural properties are studied. It is shown that the scalar field in the exterior domain is defined uniquely, while the elastic vector field in the interior domain is defined modulo Jones modes. On the basis of these results a uniqueness theorem for the solution to the inverse fluid-structure interaction problem is proved.