Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force
Authors:
Joyce R. McLaughlin and Arturo Portnoy
Journal:
Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 7277
MSC (1991):
Primary 35P20
Published electronically:
August 19, 1997
MathSciNet review:
1461976
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Abstract: Series expansions are obtained for a rich subset of eigenvalues and eigenfunctions of an operator that arises in the study of rectangular membranes: the operator is the 2D Laplacian with restorative force term and Dirichlet boundary conditions. Expansions are extracted by considering the restorative force term as a linear perturbation of the Laplacian; errors of truncation for these expansions are estimated. The criteria defining the subset of eigenvalues and eigenfunctions that can be studied depend only on the size and linearity of the perturbation. The results are valid for almost all rectangular domains.
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Additional Information
Joyce R. McLaughlin
Affiliation:
Rensselaer Polytechnic Institute, Troy, NY 12180
Email:
mclauj@rpi.edu
Arturo Portnoy
Affiliation:
Rensselaer Polytechnic Institute, Troy, NY 12180
Email:
portna@rpi.edu
DOI:
http://dx.doi.org/10.1090/S1079676297000279
PII:
S 10796762(97)000279
Keywords:
Perturbation expansion,
eigenvalue,
eigenvector,
membrane,
inverse nodal problem
Received by editor(s):
May 16, 1997
Published electronically:
August 19, 1997
Communicated by:
Michael Taylor
Article copyright:
© Copyright 1997
American Mathematical Society
