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Akustische wellen in Gebieten, die von zwei lokal gestorten parallelen ebenen begrenzt sind
Author(s) -
Faulhaber Markus,
Werner P.
Publication year - 1982
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.1670040125
Subject(s) - mathematics , uniqueness , eigenvalues and eigenvectors , mathematical analysis , laplace transform , boundary value problem , operator (biology) , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
Abstract We consider acoustic waves in domains with boundaries, coinciding with two parallel planes outside a sufficiently large sphere. Several results on spectral properties of the Laplace operator in such domains are derived and used to prove uniqueness and existence of a solution of the Dirichlet boundary value problem for the reduced wave equation under additional restrictions. In particular, a class of domains is described for which no eigenvalues are present.