Acoustic waves in perturbed periodic layer: a limiting absorption principle

Article type: Research Article

Authors: Levendorski\u{\i}, S.Z.

Affiliations: Rostov Institute of National Economy, 69 B. Sadovaya, Rostov‐on‐Don, 344798, Russia

Abstract: The acoustic wave propagator in a perturbed periodic layer 0< z< 1 is given by H=- c^{2}(x, y)\rho(x, y)\Big[\nabla \frac{1}{\rho(x, y)}\nabla\Big], where the speed of sound c and density \rho are short‐range perturbations of functions periodic in (x, y). A ‘limiting absorption principle’ for H is established between suitably weighted L_{2}‐spaces. The limiting values of the resolvent are shown to be Hölder continuous at generic points of the real axis.

Journal: Asymptotic Analysis, vol. 16, no. 1, pp. 15-24, 1998