Wave operators to a quadratic nonlinear Klein-Gordon equation in two space dimensions revisited

被引：1

作者：

Hayashi, Nakao ^{[1
]}

Naumkin, Pavel I. ^{[2
]}

Tonegawa, Satoshi ^{[3
]}

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico

[3] Nihon Univ, Dept Math, Coll Sci & Technol, Tokyo 1018308, Japan

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2012年 / 63卷 / 04期

关键词：

Nonlinear Klein-Gordon equations; Quadratic nonlinearity; Two space dimensions; GLOBAL EXISTENCE;

D O I：

10.1007/s00033-011-0183-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We continue to study the existence of the wave operators for the nonlinear Klein-Gordon equation with quadratic nonlinearity in two space dimensions (partial derivative(2)(t) - Delta + m())(2)u = lambda u(2), (t, x) is an element of R x R-2. We prove that if u(1)(+) is an element of H-3/2+3 gamma,H-1 (R-2), u(2)(+) is an element of H-1/2+3 gamma,H-1 (R-2), where gamma is an element of (0, 1/4) and the norm parallel to u(1)(+)parallel to(H13/2+gamma) + parallel to u(2)(+)parallel to(H11/2+gamma) <= rho, then there exist rho > 0 and T > 1 such that the nonlinear Klein-Gordon equation has a unique global solution u is an element of C([T, infinity); H-1/2 (R-2)) satisfying the asymptotics parallel to u(t) - u(0)(t)parallel to(H1/2) <= Ct-1/2-gamma for all t > T, where u (0) denotes the solution of the free Klein-Gordon equation.

引用

页码：655 / 673

页数：19