David Natroshvili, Tilo Arens, and Simon N. Chandler-Wilde

Uniqueness, Existence, and Integral Equation Formulations for Interface Scattering Problems

abstract:
We consider a two-dimensional transmission problem in which Helmholtz equations with different wave numbers hold in adjacent non-locally perturbed half-planes having a common boundary which is an infinite, one-dimensional, rough interface line. First a uniqueness theorem for the interface problem is proved provided that the scatterer is a lossy obstacle. Afterwards, by potential methods, the non-homogeneous interface problem is reduced to a system of integral equations and existence results are established.

Mathematics Subject Classification: 35B40, 35L05.

Key words and phrases: Interface problems, scattering, integral equations.