Cauchy problem for a nonlinear viscoelastic equation with nonlinear damping and source terms
โ Scribed by Liqing Lu; Shengjia Li
- Book ID
- 108052628
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 233 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
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๐ SIMILAR VOLUMES
For the Cauchy problem for the nonlinear wave equation with nonlinear damping and source terms we define stable and unstable sets for the initial data. We prove that, if during the evolution the solution enters into the stable set, the solution is global and we are able to estimate the decay rate of
## Abstract In this paper we consider a nonlinear wave equation with damping and source term on the whole space. For linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. The criteria to guarantee blowup of solutions with positive initial energy a