Croc, Elisabeth; Dermenjian, Yves Eigenvalues and limiting absorption principle in an acoustic strip. (Valeurs propres et principe d’absorption limite dans une bande acoustique.) (French. Abridged English version) Zbl 0878.76069 C. R. Acad. Sci., Paris, Sér. I 322, No. 11, 1113-1118 (1996). Summary: One considers the acoustic propagator \(A=-\nabla\cdot c^2\nabla\) in the strip \(\Omega=\{(x,z)\in\mathbb{R}^2\), \(0< z<H\}\). The velocity \(c\), which describes the multistratification of the strip \(\Omega\), depends for large \(|x|\) only on the variable \(z\); it is assumed to be a function in \(L^\infty(\Omega)\), bounded from below by \(c_{\min}>0\), and there exists a real number \(M\geq 0\) such that \(c(x,z)= c_1(z)\) if \(x<-M\) and \(c(x,z)= c_2(z)\) if \(x>M\). Thanks to the known results on spectral analysis, limiting absorption principle and division theorems for the free propagators \(A_j\), \(j=1,2\), associated to the velocities \(c_j\), the spectrum of \(A\) is described and a limiting absorption principle is obtained outside of a countable set \(\Gamma\). The points of \(\Gamma\) can only accumulate on the left of the thresholds of the free propagators. Cited in 1 Document MSC: 76Q05 Hydro- and aero-acoustics 35P20 Asymptotic distributions of eigenvalues in context of PDEs Keywords:acoustic propagator; multistratification; division theorems PDFBibTeX XMLCite \textit{E. Croc} and \textit{Y. Dermenjian}, C. R. Acad. Sci., Paris, Sér. I 322, No. 11, 1113--1118 (1996; Zbl 0878.76069)