**D. Natroshvili, G. Sadunishvili, I. Sigua, Z. Tediashvili**

##
Fluid-Solid Interaction: Acoustic Scattering by an Elastic Obstacle with
Lipschitz Boundary

**abstract:**

The potential method is developed for the three-dimensional interface problems
of the theory of acoustic scattering by an elastic obstacle which are also known
as fluid-solid (fluid-structure) interaction problems. It is assumed that the
obstacle has a Lipschitz boundary. The sought for field functions belong to
spaces having $L_2$ integrable nontangential maximal functions on the interface
and the transmission conditions are understood in the sense of nontangential
convergence almost everywhere. The uniqueness and existence questions are
investigated. The solutions are represented by potential type integrals. The
solvability of the direct problem is shown for arbitrary wave numbers and for
arbitrary incident wave functions. It is established that the scalar
acoustic (pressure) field in the exterior domain is defined uniquely, while the
elastic (displacement) vector field in the interior domain is defined modulo
Jones modes, in general. On the basis of the results obtained it is proved that
the inverse fluid-structure interaction problem admits at most one solution.

**Mathematics Subject Classification:**
35J05, 35J25, 35J55, 35P25, 47A40, 74F10, 74J20

**Key words and phrases:** Fluid-solid interaction, elasticity theory,
Helmholtz equation, potential theory, interface problems, steady state
oscillations