## Un opérateur à résolvante non compacte pour un problème couplé de vibrations acoustiques. (An operator with non compact resolvent for a coupled acoustic problem).(French)Zbl 0676.76076

Summary: We study the acoustic coupling between the vibrations of a gas contained in narrow channels in one direction hollowed in a porous body $$\Omega_ p$$ and in an exterior region $$\Omega_ f$$ of $${\mathbb{R}}^ 3$$ where standard acoustic holds. The associated operator is selfadjoint but has not a compact resolvent. The study of the eigenvalue problem allows us to characterize the elements of the spectrum $$\sigma$$ (A) of the operator A associated with the problem.

### MSC:

 76Q05 Hydro- and aero-acoustics 35Q99 Partial differential equations of mathematical physics and other areas of application 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation