Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Perturbation of the eigenvalues of a membrane with a concentrated mass

Authors: C. Leal and J. Sanchez-Hubert
Journal: Quart. Appl. Math. 47 (1989), 93-103
MSC: Primary 73K12; Secondary 35B25
DOI: https://doi.org/10.1090/qam/987898
MathSciNet review: 987898
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Abstract: We study a vibrating membrane with a distribution of density depending on $ \varepsilon $, which converges, as $ \varepsilon \searrow 0$, to a uniform density, plus a point mass at the origin. We establish local vibrations at the vicinity of the origin and global vibrations of the membrane. The asymptotic study for $ \varepsilon \searrow 0$ is performed using the method of matched asymptotic expansions.

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DOI: https://doi.org/10.1090/qam/987898
Article copyright: © Copyright 1989 American Mathematical Society

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