Scattering theory for a stratified acoustic strip with short- or long-range perturbations.
The authors deal with the acoustic propagator \(H=-\nabla\cdot\rho\nabla\) acting in \(L^2(\Omega)\) with \(\Omega= \Omega\times\mathbb R\), and \(\widetilde{\Omega}\) a bounded open set in \(\mathbb R^{n-1}\), \(n\geq 2\). Here \(\rho\in L^\infty(\Omega)\) and bounded below by \(c>0\). Under some additional assumptions on \(\rho\), they build free evolutions \(W_j(t)\), \(j=1,2\), such that the wave operators \(Q_j^\pm:= s-\lim_{t\to\pm\infty} e^{itH} W_j(t)\), \(j=1,2\), exist and are asymptotically complete.
scientific article; zbMATH DE number 1777449
scientific article