## Abstract and Applied Analysis

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

Xiaopan Liu

#### 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

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

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