On the Cauchy problem for a generalized Boussinesq equation
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NOTICE: This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published Journal of Computational and Applied Mathematics, Vol. 353, Issue 1. (2009). doi: 10.1016/j.jmaa.2008.12.002
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In this paper, we consider the Cauchy problem for a generalized Boussinesq equation. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive the sufficient conditions for the blow-up of the solution to the problem.
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