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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded
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by Michel Chipot and Arnaud Rougirel PDF
Trans. Amer. Math. Soc. 360 (2008), 3579-3602 Request permission

Abstract:

The aim of this work is to analyze the asymptotic behaviour of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions. In particular, in the case of a linear elliptic operator in divergence form, we prove that the sequence of the $k$-th eigenvalues convergences to the first eigenvalue of an elliptic problems set on the section of the domain. Moreover, an optimal rate of convergence of this sequence is given.
References
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Additional Information
  • Michel Chipot
  • Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
  • Email: m.m.chipot@math.unizh.ch
  • Arnaud Rougirel
  • Affiliation: Laboratoire de Mathématiques et Applications, UMR 6086, Université de Poitiers & CNRS, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86 962 Futuroscope Chasseneuil Cedex, France
  • Email: rougirel@math.univ-poitiers.fr
  • Received by editor(s): June 27, 2005
  • Received by editor(s) in revised form: April 24, 2006
  • Published electronically: January 9, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 3579-3602
  • MSC (2000): Primary 35P15, 35B40
  • DOI: https://doi.org/10.1090/S0002-9947-08-04361-4
  • MathSciNet review: 2386237