## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2012 (2012), Article ID 615345, 27 pages.

### On Existence, Uniform Decay Rates, and Blow-Up for Solutions of a Nonlinear Wave Equation with Dissipative and Source

#### Abstract

This paper studies the blow-up and existence, and asymptotic behaviors of the solution of a nonlinear hyperbolic equation with dissipative and source terms. By using Galerkin procedure and the perturbed energy method, the local and global existence of solution is established. In addition, by the concave method, the blow-up of solutions can be obtained.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2012 (2012), Article ID 615345, 27 pages.

**Dates**

First available in Project Euclid: 28 March 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1364475826

**Digital Object Identifier**

doi:10.1155/2012/615345

**Mathematical Reviews number (MathSciNet)**

MR2975269

**Zentralblatt MATH identifier**

1253.65195

#### Citation

Liu, Xiaopan. On Existence, Uniform Decay Rates, and Blow-Up for Solutions of a Nonlinear Wave Equation with Dissipative and Source. Abstr. Appl. Anal. 2012 (2012), Article ID 615345, 27 pages. doi:10.1155/2012/615345. https://projecteuclid.org/euclid.aaa/1364475826