%0 Journal Article %T A limiting absorption principle for scattering problems with unbounded obstacles %+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS) %A Bonnet-Ben Dhia, Anne-Sophie %A Tillequin, Axel %< avec comité de lecture %@ 0170-4214 %J Mathematical Methods in the Applied Sciences %I Wiley %V 24 %N 14 %P 1089--1111 %8 2001-09 %D 2001 %R 10.1002/mma.259Journal articles %X A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two-dimensional Helmholtz case. This method leads by variational means to an integro-differential formulation whose unknown is the trace of the field on an unbounded one-dimensional interface. The well-posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result--based upon some properties of a singular integral operator similar to the Hilbert transform--the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized. Copyright © 2001 John Wiley & Sons, Ltd. %G English %L hal-01008796 %U https://ensta-paris.hal.science/hal-01008796 %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2