拟线性退化抛物-双曲型方程是一类重要的混合型非线性偏微分方程，在水动力学中的多相流问题、多孔介质中的污染物迁移过程等均有广泛的应用。该方程最主要的特点是方程的类型依赖于解本身，与非退化(抛物型)和完全退化(双曲型)的情形截然不同。本项目将研究各向异性退化抛物-双曲型方程和耦合退化抛物-双曲型方程组的Dirichlet 初边值问题。我们将对方程的数学结构和退化特性做深入的分析，将处理单个方程问题的经典方法(如双变量方法、动力学方法、重整化方法等)推广至方程组的情形，推动其数学理论的成熟和应用。

Quasi-linear degenerate parabolic-hyperbolic equation is an important kind of mixed-type nonlinear partial differential equations, which has a wide range of applications in multiphase flow, the pollutant migration process and so on. The main feature of this equation is that the type of equation depends on the solution itself, totally different from the non-degenerate (parabolic) and full-degenerate (hyperbolic) cases. This project is aimed to study the initial- boundary value problems for anisotropic degenerate parabolic-hyperbolic equation and coupling degenerate parabolic-hyperbolic system. We will make an in-depth analysis of the mathematics structure and degenerate features of this equation, and, extend the classical methods to deal with scalar equations (doubling variables device, kinetic method, renormalized method etc.) to the system, hopefully enriching the mathematical theories and the applications of this equation.