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