Abstract:
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.