论文摘要
本文首先研究了带有摩擦项广义Chaplygin气体非对称Keyfitz-Kranzer方程组的Riemann解,随后研究了齐次Chaplygin气体非对称Keyfitz-Kranzer方程组Riemann解的稳定性.第一章介绍了本文的研究背景、现状以及主要内容和结构安排第二章主要研究了带有摩擦项的广义Chaplygin气体非对称Keyfitz-Kranzer方程组的Riemann问题,并得到其Riemann解的整体结构.Riemann解中包含激波,稀疏波,接触间断和δ-激波.与齐次非对称Keyfitz-Kranzer方程组不同的是非齐次非对称Keyfitz-Kranzer方程组的Riemann解是非自相似的.第三章主要研究了齐次Chaplygin气体非对称Keyfitz-Kranzer方程组Riemann解的稳定性.在对Riemann初值做一个局部小扰动下,我们构造性地得到了方程组不同结构解的显式表达式.随后通过让扰动参数趋于零得到Riemann解是稳定的.最后我们证明没有质量集中形成即使初值随ε → 0而趋于无穷.
论文目录
文章来源
类型: 硕士论文
作者: 刘继儿
导师: 郭俐辉
关键词: 非对称方程组,问题,非自相似,稳定性,狄拉克激波
来源: 新疆大学
年度: 2019
分类: 基础科学
专业: 数学
单位: 新疆大学
分类号: O175
总页数: 44
文件大小: 1922K
下载量: 12
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