一类带调和势的非线性Klein-Gordon方程的L^2-集中性质  

L^2-concentration of Blow-up Solutions for a Class of Nonlinear Klein-Gordon Equation with a Harmonic Potential

作　　者：冯远福[1] 胡丹[2] 

机构地区：[1]北京联合大学基础部,北京100101 [2]北京师范大学信息科学与技术学院,北京100875

出　　处：《工程数学学报》2009年第3期553-557,共5页Chinese Journal of Engineering Mathematics

摘　　要：Klein-Gordon方程是相对论、量子力学和量子场论中最基本的方程。本文在n维空间中讨论一类带调和势的非线性Klein-Gordon方程的初值问题,在得到其局部解存在性的基础之上,应用能量方法和微分、积分不等式技巧,得到了在一定条件下解的爆破性质,并进一步讨论了解的爆破点与L2-集中性质。The Klein-Gordon equation is the equation of motion of a quantum scalar or pseudoscalar field, a field whose quanta axe spinless particles. This paper concerns with the Cauchy problem for nonlinear Klein-Gordon equations with a harmonic potential in an n dimensional space. As the basis of this paper, the existence of local solutions of this equation has been proven. By techniques such as the energy equation, differential inequation and integral inequation.the instability and the blow-up point of the solution are obtained and the L2-concentration of the blow-up solution is established.

关 键 词：非线性KLEIN-GORDON方程 调和势 爆破 爆破点 L2-集中 

分 类 号：O175.24[理学—数学]