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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 535031, 10 pages
http://dx.doi.org/10.1155/2012/535031
Research Article

On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation

Department of Mathematics, Dicle University, 21280 Diyarbakir, Turkey

Received 4 May 2012; Accepted 11 June 2012

Academic Editor: Valery Covachev

Copyright © 2012 Hatice Taskesen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity 𝛾 | 𝑢 | 𝑝 and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.