Large data asymptotic behaviour for the generalized Boussinesq equation

Published 17 January 2008 • 2008 IOP Publishing Ltd and London Mathematical Society
, , Citation Luiz Gustavo Farah 2008 Nonlinearity 21 191 DOI 10.1088/0951-7715/21/2/001

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1 Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil

Dates

  1. Received 5 July 2007
  2. Published

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0951-7715/21/2/191

Abstract

We study the long-time behaviour of solutions (without the smallness assumption) of the initial-value problem for a generalized Boussinesq equation. Here we do the reciprocal problem of the scattering theory; we construct a solution with a given scattering state , where B(·) is the unitary group associated with the linear system and is given in suitable spaces. The arguments used are in the spirit of Côte (2006 Diff. Integral Eqns 19 163–88).

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10.1088/0951-7715/21/2/001