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Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Asymptotics of resonances in a thermoelastic model with light local mass perturbations


Authors: Natalia Babych and Johannes Zimmer
Journal: Quart. Appl. Math. 67 (2009), 311-326
MSC (2000): Primary 35P15; Secondary 34E10, 74F05
DOI: https://doi.org/10.1090/S0033-569X-09-01112-8
Published electronically: March 20, 2009
MathSciNet review: 2514637
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Abstract | References | Similar Articles | Additional Information

Abstract: The limit behaviour of a linear one-dimensional thermoelastic system with local mass perturbations is studied. The mass density is supposed to be nearly homogeneous everywhere except in an $ \varepsilon$-vicinity of a given point, where it is of order $ \varepsilon^{-m}$, with $ m \in \mathbb{R}$. The resonance vibrations of the string are investigated as $ \varepsilon\to0$. An important ingredient of the analysis is the construction of an operator in a space of higher regularity such that its spectrum coincides with that of the classical operator in linearised thermoelasticity, with a correspondence of generalised eigenspaces. The convergence of eigenvalues and eigenprojectors is established along with error bounds for two classes of relatively light mass perturbations, $ m<1$ and $ m=1$, which exhibit contrasting limit behaviour.


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Additional Information

Natalia Babych
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom

Johannes Zimmer
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom

DOI: https://doi.org/10.1090/S0033-569X-09-01112-8
Received by editor(s): November 3, 2007
Published electronically: March 20, 2009
Article copyright: © Copyright 2008 by the authors
The copyright for this article reverts to public domain 28 years after publication.

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