Euler-Poisson方程的一类爆破解和时间周期解  

On the Blowup Solutions and Time Periodic Solutions of the Euler-Poisson System

作　　者：尹永刚[1] 刘晓宁[1] 吴飘飘[1] 马柏林[1] 张景军[1] 

机构地区：[1]嘉兴学院数学系,浙江嘉兴314001

出　　处：《西南师范大学学报（自然科学版）》2014年第7期12-17,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11271162;11201185);浙江省自然科学基金项目(LQ12A01013);国家级大学生创新训练计划项目(201310354015)

摘　　要：研究了宇宙常数是负值的Euler-Poisson方程,证明了一类爆破解的存在性(对应于物理上的中心塌缩现象),并给出了具体的爆破速度;同时还证明了时间周期解的存在性.运用MATLAB数学软件对相关结果做了数值验证.Euler-Poisson system is an important model in physics,which describes the motion of a selfgravitating fluid in gaseous stars.This paper deals with the studies on the Euler-Poisson system with a cosmological negative constant.We have obtained the existence of blowup solutions（this fact is related to the core collapse phenomenon in physics）,given the detailed blowup rate,and also proved the existence of time periodic solutions for this system.By means of MATLAB,the results are tested numerically.

关 键 词：EULER-POISSON方程 爆破解 周期解 

分 类 号：O175.2[理学—数学]