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.


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