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Mixed boundary value problems of diffraction by a half‐plane with an obstacle perpendicular to the boundary
Author(s) -
Castro Luis P.,
Kapanadze David
Publication year - 2013
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.2900
Subject(s) - mathematics , boundary value problem , helmholtz equation , mathematical analysis , sobolev space , operator (biology) , boundary (topology) , plane (geometry) , diffraction , geometry , quantum mechanics , biochemistry , chemistry , physics , repressor , transcription factor , gene
The paper is devoted to the analysis of wave diffraction problems modeled by classes of mixed boundary conditions and the Helmholtz equation, within a half‐plane with a crack. Potential theory together with Fredholm theory, and explicit operator relations, are conveniently implemented to perform the analysis of the problems. In particular, an interplay between Wiener–Hopf plus/minus Hankel operators and Wiener–Hopf operators assumes a relevant preponderance in the final results. As main conclusions, this study reveals conditions for the well‐posedness of the corresponding boundary value problems in certain Sobolev spaces and equivalent reduction to systems of Wiener–Hopf equations. Copyright © 2013 John Wiley & Sons, Ltd.