论文标题
不变特征的应用在没有梯度灾难的解决方案的构建中
Application of invariants of characteristics to construction of solutions without gradient catastrophe
论文作者
论文摘要
考虑到等敏气动力学方程的一维方程系统。该系统的特征的一阶不变性被分类。特征的二阶不变性被分类用于多变态过程。描述了Darboux集成系统的无限序列。提出了没有梯度灾难的平滑解决方案的构建方法。提出了没有梯度灾难的解决方案的例子。
The one-dimensional system of equations of isentropic gas dynamics is considered. First-order invariants of characteristics of this system are classified. Second-order invariants of characteristics are classified for polytropic processes. The infinite sequence of Darboux integrable systems is described. The approach to construction of smooth solutions without gradient catastrophe is proposed. Examples of solutions without gradient catastrophe are presented.
