## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 535031, 10 pages.

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

Hatice Taskesen, Necat Polat, and Abdulkadir Ertaş

#### Abstract

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity $\gamma {|u|}^{p}$ 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.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 535031, 10 pages.

**Dates**

First available in Project Euclid: 5 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1365174054

**Digital Object Identifier**

doi:10.1155/2012/535031

**Mathematical Reviews number (MathSciNet)**

MR2947731

**Zentralblatt MATH identifier**

1246.35184

#### Citation

Taskesen, Hatice; Polat, Necat; Ertaş, Abdulkadir. On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 535031, 10 pages. doi:10.1155/2012/535031. https://projecteuclid.org/euclid.aaa/1365174054