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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Spectrum of the wave equation with Dirac damping on a non-compact star graph
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by David Krejčiřík and Julien Royer
Proc. Amer. Math. Soc. 151 (2023), 4673-4691
DOI: https://doi.org/10.1090/proc/16412
Published electronically: May 12, 2023

Abstract:

We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem admits an abrupt change in its spectral properties for a special coupling related to the number of graph edges. As an application, we show that the evolution problem is highly unstable for the critical couplings. The relationship with the Dirac equation in non-relativistic quantum mechanics is also mentioned.
References
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Bibliographic Information
  • David Krejčiřík
  • Affiliation: Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
  • Email: david.krejcirik@fjfi.cvut.cz
  • Julien Royer
  • Affiliation: Institut de mathématiques de Toulouse, Université Toulouse 3, 118 route de Narbonne, F-31062 Toulouse cedex 9, France
  • MR Author ID: 846278
  • Email: julien.royer@math.univ-toulouse.fr
  • Received by editor(s): May 23, 2022
  • Received by editor(s) in revised form: January 4, 2023, and January 17, 2023
  • Published electronically: May 12, 2023
  • Additional Notes: The first author was supported by the EXPRO grant No. 20-17749X of the Czech Science Foundation. The second author was supported by the ANR LabEx CIMI (grant ANR-11-LABX-0040) within the French State Programme “Investissements d’Avenir”.
  • Communicated by: Tanya Christiansen
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4673-4691
  • MSC (2020): Primary 47A10, 47B44, 35R02, 35L05
  • DOI: https://doi.org/10.1090/proc/16412
  • MathSciNet review: 4634873