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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Evolution of the radius of spatial analyticity for the periodic BBM equation
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by A. Alexandrou Himonas and Gerson Petronilho PDF
Proc. Amer. Math. Soc. 148 (2020), 2953-2967 Request permission

Abstract:

The Cauchy problem of the Benjamin-Bona-Mahony (BBM) equation with initial data $u_0$ that are analytic on the torus and have uniform radius of analyticity $r_0$ is considered, and the evolution of the radius of spatial analyticity $r(t)$ of the solution $u(t)$ at any future time $t$ is examined. It is shown that the size of the radius of spatial analyticity persists for some time and after that it evolves in a such a way that its size at any time $t$ is bounded below by $c t^{-1}$ for some $c>0$. The optimality of this bound remains an open question.
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Additional Information
  • A. Alexandrou Himonas
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 86060
  • Email: himonas.1@nd.edu
  • Gerson Petronilho
  • Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP 13565-905, Brazil
  • MR Author ID: 250320
  • Email: gerson@dm.ufscar.br
  • Received by editor(s): January 14, 2019
  • Received by editor(s) in revised form: November 16, 2019
  • Published electronically: February 26, 2020
  • Additional Notes: The first author was partially supported by a grant from the Simons Foundation (#524469)
    The second author was partially supported by grant 303111/2015-1, CNPq, and grant 2012/03168-7, São Paulo Research Foundation (FAPESP)
  • Communicated by: Catherine Sulem
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 2953-2967
  • MSC (2010): Primary 35Q53, 37K10
  • DOI: https://doi.org/10.1090/proc/14942
  • MathSciNet review: 4099783