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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the wave operator for the generalized Boussinesq equation


Authors: Luiz Gustavo Farah and Lucas C. F. Ferreira
Journal: Proc. Amer. Math. Soc. 140 (2012), 3055-3066
MSC (2010): Primary 35Q35; Secondary 35B40, 35P25
Published electronically: December 28, 2011
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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
Email: lgfarah@gmail.com

Lucas C. F. Ferreira
Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, CEP 13083-859, Campinas-SP, Brazil
Email: lcff@ime.unicamp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11131-6
PII: S 0002-9939(2011)11131-6
Keywords: Boussinesq equation, inverse scattering, large data, Lorentz spaces.
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.