A parametric limiting absorption problem with degeneration

Abstract

We are concerned with acoustic waves propagation in inhomogeneous media in the case where density ρ(x), being independent of r=|x| and depending on a parameter τ, can vanish on some domains of R3 for some isolated value τ=τ0. We investigate the behavior of solutions of wave equation as τ→τ0, prove the limiting absorption principle for τ=τ0, and apply the obtained results to a wave fronts propagation problem.