## Asymptotics and spectral properties of the acoustic vibrations of a body perforated by narrow channels.(English)Zbl 0616.76094

Using homogenization asymptotic techniques, we study the acoustic vibrations of a gas contained in narrow channels hollowed in a solid body (and maybe some outer region surrounding the body). Only solutions depending on time by the factor exp(-i$$\omega$$ t) are considered. The homogenized equations describing the asymptotics of the phenomena are not elliptic, as only derivatives in the direction of the channels appear. In the non-dissipative case, the associated operator is self-adjoint; according to the geometric configuration, it may exhibit eigenvalues with finite or infinite multiplicity or a continuous spectrum. The boundary conditions and the corresponding boundary layers between the body and the outer fluid are studied.

### MSC:

 76Q05 Hydro- and aero-acoustics 76N99 Compressible fluids and gas dynamics