Klein-Gordon-Hartree方程驻波的不稳定性  

Instability for the Standing Wave of Klein-Gordon-Hartree Equation

作　　者：李晓光[1] 

机构地区：[1]四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2012年第3期425-429,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11071177);四川省杰出青年基金(2012JQ0011)资助项目

摘　　要：研究如下Klein-Gordon-Hartree方程的驻波2u/t2-△u+ωu-(|x|-γ*|u|2)u=0,x∈RN.首先,通过构造合理的约束变分问题建立基态驻波解的存在性及其变分特征.然后,以变分特征为基础,证明存在一个Klein-Gordon-Hartree方程的解序列,其初始条件充分接近基态驻波,同时解在有限时间爆破,从而得到基态驻波的不稳定性.The aim of this paper is to study the standing wave of the Klein-Gordon-Hartree equation2u t2-△u＋ω u-（｜x｜^-γ＊ ｜u｜2）u=0,x∈RN.Firstly,a constrained variational problem is constructed to get the existence and variational characterization of the ground state.Moreover,based upon the variational characterization of the ground state,it is proved that there exists a sequence of solutions of the Klein-Gordon-Hartree equation such that the initial data of the solutions are close to the ground state and the solutions blow up in finite time.Hence the instability of the standing wave is obtained.

关 键 词：Klein-Gordon-Hartree方程 驻波 基态 不稳定 

分 类 号：O175.24[理学—数学]