Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Kawahara, Yuichiro²  Sunagawa, Hideaki¹ 

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

[2] Doshisha Jr & Senior High Sch, Sakyo Ku, Kyoto 6068558, Japan

关键词: Nonlinear Klein-Gordon equations;    Mass resonance;    Global solution;   

DOI  :  10.1016/j.jde.2011.04.001

来源: Elsevier

【 摘 要 】

We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses m(1), m(2) satisfying the resonance relation m(2) = 2m(1) > 0. We introduce a structural condition on the non- linearities under which the solution exists globally in time and decays at the rate O(vertical bar t vertical bar(-1)) as t -> +/-infinity in L(infinity). In particular, our new condition includes the Yukawa type interaction, which has been excluded from the null condition in the sense of J.-M. Delort, D. Fang and R. Xue Delort, D. Fang, R. Xue, Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions, J. Funct. Anal. 211 (2004) 288-3231. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free