Abstract
We consider the problem of diffraction of an acoustic wave on a set of small obstacles (cavities) with the boundary condition of the third kind on the obstacle boundary and the radiation condition at infinity. It is assumed that the obstacle diameters converge and for each obstacle the distance to the nearest obstacle is much greater than the obstacle diameter. We establish the closeness between the solutions to the boundary value problems in a domain with obstacles and the solution to the homogenized problem and prove the convergence of scattering frequencies to the scattering frequencies of the limiting problem with potential.
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