## 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
Standing waves and global existence for the nonlinear wave equation with potential and damping terms
β Scribed by Yi Jiang; Zaihui Gan; Yiran He
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 582 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la
The long-time behavior of the wave equation with nonmonotone interior damping is considered. It is shown that the semigroup generated by this equation possesses a global attractor in H 1 0 (β¦ ) Γ L 2 (β¦ ).
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