# Scattering Theory for a Stratiﬁed Acoustic Strip with Short- or Long-Range Perturbations

### Viorel Iftimie

Romanian Academy, Bucharest, Romania### Elizabeth Croc

CMI-Université d'Aix-Marseille I, France

## Abstract

We consider the acoustic propagator *H* = −∇ · _ρ_∇ acting in _L_2 (Ω) with Ω := Ω' × ℝ and Ω' a bounded open set in ℝ_n_−1, *n* ≥ 2. The real-valued function *ρ* belongs to _L_∞(Ω), and is bounded from below by *c* > 0. We assume there exist two strictly positive constants *c_1 and c_2 and two perturbations, δS of short-range type and δL of long-range type, such that ρ = cj + δS + δL on Ω_j := {(x', xn) ∈ Ω|(−1)j xn > 0}, j = 1, 2. We build two modiﬁed free evolutions U__j(t), j = 1, 2, such that the wave operators Ω±_j* :=

*s*− lim_t_→±∞

*eitH*

*U__j*(

*t*),

*j*= 1, 2, exist and are asymptotically complete.