Examples of embedded eigenvalues for problems in acoustic waveguides

Mathematical Methods in the Applied Sciences

Volumn 21, Issue 6, 1998, Pages 479-488

  Groves, M D ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; MATHEMATICAL OPERATORS; VARIATIONAL TECHNIQUES; VECTORS; WAVEGUIDES;

ANTISYMMETRIC EIGENVECTOR; NEUMANN LAPLACIAN;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0032047121     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1476(199804)21:6<479::AID-MMA950>3.0.CO;2-V     Document Type: Article

References (8)

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3. Evans, D. V., Levitin, M. and Vassiliev, D., 'Existence theorems for trapped modes', J. Fluid Mech. 261, 21-31 (1994).
4. Evans, D. V., Linton, C. M. and Ursell, F., 'Trapped mode frequencies embedded in the continuous spectrum', Quart. J. Mech. Appl. Math. 46, 253-274 (1993).
5. Goldstein, C. I., 'Eigenfunction expansions associated with the Laplacian for certain domains with infinite boundaries I', Trans. Amer. Math. Soc. 135, 1-31 (1969).
6. 2u + λu = 0 when the boundary conditions are given on semi-infinite domains', Proc. Camb. Phil. Soc. 49, 668-684 (1953).
7. Parker, R. and Stoneman, S. A. T, 'The excitation and consequences of acoustic resonances in enclosed fluid flow around solid bodies', Proc. Inst. Mech. Engrs. 203, 9-19 (1989).
8. Wilcox, C. H., Scattering Theory for the d' Alambert Equation in Exterior Domains. Springer, Berlin, 1975.