Spectral analysis of the acoustic propagator in a multistratified domain
A selfadjoint operator \(H\) modeling the propagation of aoustic waves in a multistratified domain \(\Omega\) is considered. The operator \(H\) is of the form \(-\nabla c(x)\nabla\) \((c\) is the propagation velocity depending on the stratification of \(\Omega)\). This model with some perturbations in a more general situation is studied. The spectrum of \(H\) is calculated and the limiting absorption principle in an optimal scale of suitable Besov spaces is established by the conjugate operator method. A formula for the spectrum of \(H\) is obtained, and the accumulation of eigenvalues of \(H\) and the continuity of the spectrum are analyzed.
scientific article; zbMATH DE number 1218231