Semilinear hyperbolic systems violating the null condition

被引：17

作者：

Katayama, Soichiro ^{[1
]}

Matoba, Toshiaki ^{[2
]}

Sunagawa, Hideaki ^{[3
]}

机构：

[1] Wakayama Univ, Dept Math, Wakayama 6408510, Japan

[2] Osaka Prefectural Tennoji High Sch, Abeno Ku, Osaka 5450005, Japan

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

来源：

MATHEMATISCHE ANNALEN | 2015年 / 361卷 / 1-2期

关键词：

NONLINEAR SCHRODINGER-EQUATIONS; KLEIN-GORDON SYSTEMS; WAVE-EQUATIONS; GLOBAL-SOLUTIONS; ASYMPTOTIC-BEHAVIOR; EXISTENCE; DECAY;

D O I：

10.1007/s00208-014-1071-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition related to the weak null condition. For two-component systems satisfying this condition, we also observe a new kind of asymptotic behavior: Only one component is dissipated and the other one behaves like a non-trivial free solution in the large time.

引用

页码：275 / 312

页数：38

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