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The low frequency limit for time‐harmonic acoustic waves
Author(s) -
Picard R.,
Leis R.
Publication year - 1986
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.1670080128
Subject(s) - mathematics , uniqueness , eigenvalues and eigenvectors , mathematical analysis , limit (mathematics) , boundary value problem , scalar (mathematics) , convergence (economics) , zero (linguistics) , harmonic , dirichlet boundary condition , dirichlet problem , geometry , physics , acoustics , linguistics , philosophy , quantum mechanics , economics , economic growth
The question of convergence of the solution of the exterior Dirichlet boundary value problem of the first order system of linearized acoustics as the frequency ω tends to zero is considered. The particular difficulty of having zero as an eigenvalue is handled by introducing certain scalar characteristics that — if prescribed — imply uniqueness in the limit case ω = 0. Convergence to the static solution in a weighted L 2 ‐space is shown. Eventually the convergence result obtained can be extended to a larger class of boundary value problems of Mathematical Physics due to the structure of the argument.