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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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Lyapunov-type characterisation of exponential dichotomies with applications to the heat and Klein–Gordon equations
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by Gong Chen and Jacek Jendrej PDF
Trans. Amer. Math. Soc. 372 (2019), 7461-7496 Request permission

Abstract:

We give a sufficient condition for the existence of an exponential dichotomy for a general linear dynamical system (not necessarily invertible) in a Banach space, in discrete or continuous time. We provide applications to the backward heat equation with a potential varying in time, and to the heat equation with a finite number of slowly moving potentials. We also consider the Klein–Gordon equation with a finite number of potentials whose centres move at sublight speed with small accelerations.
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Additional Information
  • Gong Chen
  • Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
  • MR Author ID: 1003678
  • Email: gc@math.toronto.edu
  • Jacek Jendrej
  • Affiliation: CNRS and Université Paris 13, LAGA, UMR 7539, 99 avenue J.-B. Clément, 93430 Villetaneuse, France
  • MR Author ID: 1060238
  • Email: jendrej@math.univ-paris13.fr
  • Received by editor(s): January 2, 2019
  • Received by editor(s) in revised form: May 30, 2019
  • Published electronically: August 28, 2019
  • Additional Notes: Part of this work was completed when the second author was visiting the University of Chicago Mathematics Department and the University of Toronto Mathematics Department. He was also partially supported by the ANR-18-CE40-0028 project ESSED
    The authors would like to thank the Beijing International Center for Mathematical Research, where this work was finished.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7461-7496
  • MSC (2010): Primary 35B40; Secondary 37D99
  • DOI: https://doi.org/10.1090/tran/7923
  • MathSciNet review: 4024558