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Decay and Scattering of Small Solutions of a Generalized Boussinesq Equation

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
147
Issue
1
Identifiers
DOI: 10.1006/jfan.1996.3052

Abstract

Abstract We study the long-time behavior of small solutions of the initial-value problem for a generalized Boussinesq equation. We obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations; that is, the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem. Under certain hypotheses, we can construct a scattering operator for the Boussinesq equation which carries a neighborhood of 0 in the energy space Xinto X.

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