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A limiting absorption principle for scattering problems with unbounded obstacles
Author(s) -
BonnetBendhia AnneSophie,
Tillequin Axel
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.259
Subject(s) - limiting , scattering , helmholtz free energy , helmholtz equation , operator (biology) , mathematics , class (philosophy) , mathematical analysis , harmonic , absorption (acoustics) , field (mathematics) , pure mathematics , physics , computer science , quantum mechanics , boundary value problem , optics , chemistry , transcription factor , mechanical engineering , biochemistry , repressor , artificial intelligence , engineering , gene
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.