煤矿瓦斯爆炸事故一直是矿井安全生产的重大威胁之一。尽管在巷道中布置了阻隔爆设施，但并没有起到应有的作用，有的甚至加强了爆炸强度。对此方面的研究，国内外基本上都是把巷道假设成一维直管道，而没有对瓦斯爆炸传播过程中起决定作用的火焰面和冲击波等自由界面的形成与运动规律，尤其在巷道障碍物和复杂网络化管道影响下的运动规律和相关理论进行深入研究。本项目将致力于这两个自由界面形成与运动的数学建模与分析；探讨瓦斯爆炸初期可燃混气燃烧的多流体模型及相关多相流模型的数学理论与数值分析；建立可燃混气从燃烧到爆燃再到爆轰的跨音速传播过程的数学模型与分析；并模拟两波之间的时间间隔和间距变化，预测冲击波传播的总距离及安全范围，为有效的进行抑爆和阻隔爆技术提供理论支撑。因此，通过该项目，我们既能服务需求，又能抽象出新颖的数学问题，还能创建具有特色的研究方法和一般理论，对丰富和发展偏微分方程理论具有十分重要的意义。

Gas explosion is one of the significant threats to mine safety production. Despite in the roadway arranging the flameproof devices, the devices do not work effectively, some even strengthen the bursting strength. In this area of research, the studies at home and abroad assume the roadway into a one-dimensional branch pipe basically, without any further investigations on the formation and motion law of the free interfaces which play the decisive role, like flame surface and shock wave etc. in the process of gas explosion propagation, especially the motion law and related theory under the influence of roadway obstacles and complex pipe network. In this project, we will aim to build the mathematical modeling and analysis of two free interfaces' formation and movement, to explore the mathematical theory and numerical analysis of multi-fluid model for combustible mixed gas and the relevant multi-phase flow model in early gas explosion, to establish the mathematical model and analysis of the transonic propagative process for combustible mixed gas that combustion pass to deflagration, then turn to detonation, and to simulate the time interval and distance changes between the two waves, to predict the total distance and safety range for the shock wave propagation, to provide theoretical support for explosion suppression and flameproof technology. Therefore, via this project, we can service requirements, abstract the novel mathematical problems, and create distinctive research method and the general theory. It is of great significance to enrich and develop the theory of partial differential equations.