Diffraction by an impedance strip I. Reducing diffraction problem to Riemann–Hilbert problems

Abstract

A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced to two matrix Riemann-Hilbert problems with exponential growth of unknown functions (for the symmetrical part and for the antisymmetrical part). For this, the Wiener--Hopf problems are formulated, they are reduced to auxiliary functional problems by applying the embedding formula, and finally the Riemann-Hilbert problems are formulated by applying the Hurd's method. In the second part the Riemann-Hilbert problems will be solved by a novel method of OE-equation.