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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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On the wave operator for the generalized Boussinesq equation
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by Luiz Gustavo Farah and Lucas C. F. Ferreira PDF
Proc. Amer. Math. Soc. 140 (2012), 3055-3066 Request permission

Abstract:

We study the asymptotic behavior of solutions for the generalized Boussinesq equation in a singular framework. We construct a wave operator (inverse scattering) for large profiles $\vec {h}$ belonging to an infinite mass framework based on weak $L^{p}$-spaces. Our solutions converge towards the prescribed scattering state with a polynomial rate.
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Additional Information
  • Luiz Gustavo Farah
  • Affiliation: Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil
  • MR Author ID: 831713
  • Email: lgfarah@gmail.com
  • Lucas C. F. Ferreira
  • Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, CEP 13083-859, Campinas-SP, Brazil
  • MR Author ID: 795159
  • Email: lcff@ime.unicamp.br
  • Received by editor(s): October 1, 2010
  • Received by editor(s) in revised form: March 16, 2011
  • Published electronically: December 28, 2011
  • Additional Notes: The first author was partially supported by FAPEMIG and CNPq, Brazil.
    The second author was supported by CNPq and FAPESP, Brazil
  • Communicated by: Walter Craig
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 3055-3066
  • MSC (2010): Primary 35Q35; Secondary 35B40, 35P25
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11131-6
  • MathSciNet review: 2917079