×

Scattering of solutions of nonlinear Klein-Gordon equations in higher space dimensions. (English) Zbl 0566.35078

Recent topics in nonlinear PDE, North-Holland Math. Stud. 98, 221-239 (1984).
[For the entire collection see Zbl 0549.00011.]
This paper is devoted to the theory of scattering for the nonlinear Klein-Gordon equation \(u_{tt}-\Delta u+m^ 2u+| u|^{p-1}u=0\) in space dimension \(n\geq 3\), with \(4/(n-1)<p-1<4/(n-2).\) It is a sequel of a previous paper by the first author [see J. Math. Soc. Japan 35, 521- 538 (1983; Zbl 0554.35095)], where the same problem was treated for \(n=3\), and extends the results of the latter to higher dimensions, under the assumption quoted above, plus additional complicated restrictions for \(n\geq 11\). The reader is sent back to the previous abstract for a description of the results as well as for an additional bibliography.
Reviewer: J.Ginibre

MSC:

35P25 Scattering theory for PDEs
35L70 Second-order nonlinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
47A40 Scattering theory of linear operators