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
A Pair of Zakharov Equations with Collisional Damping and the Motion of Langmuir Soliton
β Scribed by J. C. Bhakta
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 226 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0005-8025
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## Abstract In this paper, we consider the nonβlinear wave equation __a__,__b__>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on __Ξ±__, __m__, and __p__, we give precise decay rates for the solution. In particular, we show that for __m__=0, the decay is ex
## Communicated by E. Meister We deal with the system of equations of motion of a viscous barotropic fluid. The system contains an artificial viscosity, which depends on the density p of the fluid and is identically equal to zero for p E (0, p 2 ) (where p2 is a given positive number). If p2 is ch