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Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves
Author(s) -
Charão Ruy Coimbra,
Menzala Gustavo Perla
Publication year - 1996
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/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4
Subject(s) - scattering , mathematics , isotropy , infinity , plane (geometry) , mathematical analysis , class (philosophy) , complex plane , space (punctuation) , function (biology) , physics , geometry , quantum mechanics , linguistics , philosophy , artificial intelligence , evolutionary biology , computer science , biology
We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real‐valued function q ( x ) (or q ( x,t )). The medium is assumed to be isotropic and occupies the whole space Ω = ℝ 3 . We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.