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Study of generalized eigenfunctions of a perturbed isotropic elastic half‐space
Author(s) -
Dermenjian Yves,
Gaitan Patricia
Publication year - 2000
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(20000525)23:8<685::aid-mma109>3.0.co;2-i
Subject(s) - mathematics , eigenfunction , isotropy , mathematical analysis , operator (biology) , bounded function , boundary value problem , perturbation (astronomy) , boundary (topology) , eigenvalues and eigenvectors , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
We consider the self‐adjoint operator governing the propagation of elastic waves in a perturbed isotropic half‐space (perturbation with compact support of a homogeneous isotropic half‐space) with a free boundary condition. We propose a method to obtain, numerical values included, a complete set of generalized eigenfunctions that diagonalize this operator. The first step gives an explicit representation of these functions using a perturbative method. The unbounded boundary is a new difficulty compared with the method used by Wilcox [25], who set the problem in the complement of bounded open set. The second step is based on a boundary integral equations method which allows us to compute these functions. For this, we need to determine explicitly the Green's function of ( A 0 – ω 2 ), where A 0 is the self‐adjoint operator describing elastic waves in a homogeneous isotropic half‐space. Copyright © 2000 John Wiley & Sons, Ltd.