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The elastic echo problem
Author(s) -
Mabrouk Mongi,
Helali Zouheir
Publication year - 2002
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.345
Subject(s) - isotropy , mathematics , echo (communications protocol) , homogeneous , forcing (mathematics) , field (mathematics) , displacement field , boundary (topology) , mathematical analysis , linear elasticity , displacement (psychology) , boundary value problem , scattering , physics , pure mathematics , optics , combinatorics , thermodynamics , psychology , computer network , finite element method , computer science , psychotherapist
Abstract We consider a homogeneous isotropic unbounded linear elastic medium Ω⊂ℝ 3 , having a free boundary Γ. A forcing f ( t , x ) creates an incident displacement field u 0 ( t , x ). This primary field is scattered by Γ giving rise to a secondary field or echo, for which we determine the asymptotic behaviour in time. These results are obtained via the use of an tension of the time‐dependent scattering theory of C. Wilcox. Copyright © 2003 John Wiley & Sons, Ltd.