气体动力学等熵流2个疏散波的相互作用

Interaction between two rarefaction waves for gas dynamic isentropic equatins

考虑气体动力学中等熵流前向中心疏散波与后向中心疏散波的相互作用问题.借助特征分析法,对在相互作用区域上形成的Goursat问题,首先证明了当其特征边值不出现真空状态时,在相互作用的任何区域内也不会出现真空;同时证明了该问题存在唯一的光滑解.进而获得两疏散波相互作用的结果为相互穿透或在穿透过程中出现真空.

The interaction between forward and backward centred rarefaction waves for gas dynamic isentropic system is onsidered. For the Goursat problem developed in the domain of the interaction, with the help of characteristic analysis, it is proved that there will never appear vacuum in the field of interaction when there is no vacuum on the characteristic boundary. Meanwhile, the existence and uniqueness of the smooth solution is obtained. Further, the result of interaction for two rarefaction waves is presented, that is they penetrate each other or the vacuum appears in the process of the penetration.