P-方程组活塞问题大疏散波的存在性

发布时间：2018-01-01 06:17

本文关键词：P-方程组活塞问题大疏散波的存在性　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：有一个水平放置无限长的均匀截面的细长管,管内充满了静止气体,中间有活塞.当活塞以一定速度向左运动时,活塞的运动必然导致细长管内气体的运动.当气体初始状态和活塞运动速度满足适当条件时,我们用间断追踪法证明了 P-方程组的初边值问题描述的该活塞问题有包含大疏散波的整体解.本文的主要内容包括:将问题转化到拉格朗日坐标下;通过隐函数定理证明各种黎曼问题的可解性;求解各种典型的黎曼问题得到波之间的相互作用估计;选择恰当的权构造Glimm泛函得到Glimm泛函的递减性.本文为了处理弱波与大疏散波的相互作用,对Glimm泛函作出适当的修正.
[Abstract]:There is a slender tube with an infinitely long uniform section horizontally filled with static gas and a piston in the middle. When the piston moves to the left at a certain speed. The movement of the piston will inevitably lead to the movement of the gas in the slender tube. When the initial state of the gas and the velocity of the piston motion meet the appropriate conditions. By using the discontinuous tracing method, we prove that the piston problem described by the initial-boundary value problem of the P- equations has a global solution containing large evacuation waves. The main contents of this paper are as follows: transform the problem to Lagrange coordinates; The solvability of various Riemannian problems is proved by implicit function theorem. Some typical Riemannian problems are solved to estimate the interaction between waves. In order to deal with the interaction between weak wave and large evacuation wave, the Glimm functional is modified appropriately in this paper.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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