一维相对论Euler方程组活塞问题激波解的整体存在性  

Global existence of shock front solution to 1-D piston problem of relativistic Euler equations

作　　者：豆艳萍[1] 王斌[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2016年第4期572-588,共17页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11001164;11201289)

摘　　要：研究等熵流相对论Euler方程组的一维活塞问题,证明了当活塞速度是一个常数的扰动时其激波解的整体存在性.通过采用改进的Glimm格式构造问题的近似解,然后对基本波的相互作用作出精确的估计,最后构造Glimm泛函并证明其单调性.In this paper, we consider a 1-D piston problem of isentropic relativistic Euler equations, and we prove that when the velocity of the piston is small pertur- bation of constant, the corresponding piston problem admits a global shock front solution. First, we use the improved Glimm scheme to construct the approximate solution of this problem. Then, we establish precise estimates to the interactions of elementary waves. At last, we construct the Glimm functional and prove its monotonicity.

关 键 词：等熵流相对论Euler方程组 活塞问题 激波解 Glimm格式 

分 类 号：O175[理学—数学]