Based on the prerequisite of system resonance, this thesis obtains the sufficient condition of system stability using quasi-linear theory and brings forward the criterions of the system stability.

Meanwhile, many phenomena such as chaotic and quasi-period movement that are not interpreted by linear theory appear and bring about a lot of serious accidents.

Following the theory on characteristics of first order quasi-linear partial differential equations, classification of the balance equations for two-phase flow in interior ballistics is discussed.