Differential and Integral Equations

Global nonexistence of positive initial-energy solutions of a system of nonlinear wave equations with damping and source terms

Belkacem Said-Houari

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Abstract

This work is concerned with a system of nonlinear wave equations with nonlinear damping and source terms acting in both equations. We will prove that the solution of our considered system blows up in finite time provided that the initial data are large enough. This result extends a previous result in [1] to a large class of initial data. The key ingredient in the proof is a method used in [25] with necessary modifications imposed by the nature of our problem.

Article information

Source
Differential Integral Equations, Volume 23, Number 1/2 (2010), 79-92.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019388

Mathematical Reviews number (MathSciNet)
MR2588803

Zentralblatt MATH identifier
1240.35342

Subjects
Primary: 35L05: Wave equation 35L20: Initial-boundary value problems for second-order hyperbolic equations 58G16

Citation

Said-Houari, Belkacem. Global nonexistence of positive initial-energy solutions of a system of nonlinear wave equations with damping and source terms. Differential Integral Equations 23 (2010), no. 1/2, 79--92. https://projecteuclid.org/euclid.die/1356019388


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