Introduction to scattering for radial 3D NLKG below energy norm. (English) Zbl 1196.35151
The initial value problem for the equation \(u_{tt}-\Delta u+u+\left|u\right|^{p-1}u=0\) is discussed. The author proves global well-posedness of the problem in \(H^{s}(\mathbb R^3)\times H^{s-1}(\mathbb R^3)\) and existence of a scattering state as a limit of the strong solution for \(s\in (s(p),1)\) and for radial data.
Reviewer: Marie Kopáčková (Praha)
MSC:
| 35P25 | Scattering theory for PDEs |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 35B45 | A priori estimates in context of PDEs |
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