On decay and blow-up of solutions for a system of nonlinear wave equations
- 作者：Shun-Tang Wu stwu@ntut.edu.tw
- 关键词：Blow-up ; Asymptotic behavior ; Decay rate ; Global existence ; Life span ; Nonlinear damping ; Nonlinear wave equations
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2012
- 期刊代码：76_0022247x
- 类别：mt
- 出版时间：1 October, 2012
- 卷：394
- 期：1
- 页码：360-377
- 文件大小：295 K
摘要
The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with the nonlinear damping and the source terms in a bounded domain is considered. We prove that, under suitable conditions on the nonlinearity of the damping and the source terms and certain initial data in the stable set and for a wider class of relaxation functions, the decay estimates of the energy function is exponential or polynomial depending on the exponents of the damping terms in both equations by using Nakao鈥檚 method. Conversely, for certain initial data in the unstable set, we obtain the blow-up of solutions in finite time when the initial energy is nonnegative. This improves earlier results in the literature.