Asymptotic splitting of boundary-value problems for the Helmholtz equation in a strip with “permeable” boundaries

This paper is devoted to a boundary-value problem in a strip for the Helmholtz equation. This problem is a mathematical model of a hydro-acoustic waveguide with a permeable boundary. The boundary condition involves a translation-invariant operator symbolizing impendance. It is assumed that the coefficient of the Helmholtz equation varies slowly along the strip. Theorems on the unique solubility of the problem are proved, asymptotic formulae (with respect to the slowness parameter) are derived for its solution, and the practical significance of the results is discussed.