Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions

被引：11
|
作者：
Hayashi, Nakao [1 ]
Naumkin, Pavel I. [2 ]
机构：
[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan
[2] Univ Nacl Autonoma Mexico, Inst Matemat, Michoacan 58089, Mexico
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 244卷 / 01期
关键词：
asymptotics of solutions; nonlinear Klein-Gordon equations; scattering operator; higher space; dimensions; power nonlinearities;
D O I：
10.1016/j.jde.2007.10.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space H(beta, 1) with beta = max(3/2, 1 + 2/n) for the nonlinear Klein-Gordon equation with a power non-linearity u(tt) - Delta u + u = mu vertical bar u vertical bar(sigma -1)u, (t, x) epsilon R x R(n) where 1 + 4/n+2 < sigma < 1 + 4/n for n >= 3, mu epsilon C. (C) 2007 Elsevier Inc. All rights reserved.
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页码：188 / 199
页数：12
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