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Spectral convergence for vibrating systems containing a part with negligible mass
Author(s) -
Pérez Eugenia
Publication year - 2005
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.610
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , eigenvalues and eigenvectors , dimension (graph theory) , space (punctuation) , mathematical analysis , operator (biology) , order (exchange) , boundary (topology) , boundary value problem , convergence (economics) , pure mathematics , linguistics , philosophy , physics , biochemistry , chemistry , finance , repressor , quantum mechanics , transcription factor , economics , gene , economic growth
We consider a set of Neumann (mixed, respectively) eigenvalue problems for the Laplace operator. Each problem is posed in a bounded domain Ω R of ℝ n , with n =2,3, which contains a fixed bounded domain B where the density takes the value 1 and 0 outside. Ω R has a diameter depending on a parameter R , with R ⩾1, diam(Ω R ) →∞ as R →∞ and the union of these sets is the whole space ℝ n (the half space { x ∈ℝ n / x n <0}, respectively). Depending on the dimension of the space n , and on the boundary conditions, we describe the asymptotic behaviour of the eigenelements as R →∞. We apply these asymptotics in order to derive important spectral properties for vibrating systems with concentrated masses. Copyright © 2005 John Wiley & Sons, Ltd.