本项目主要针对浅水波理论中修正的b-family方程，广义的双组分DGH方程组和非线性双组份水波方程组这三类方程进行研究。在项目的实施中，将寻求新的数学工具和方法，包括在b-family方程中利用加权函数、广义的双组分DGH方程组中构造新函数、非线性双组份水波方程组中建立与参数相关的卷积估计等来解决方程解的爆破和衰减持续性等问题，这将有利于对非线性浅水波方程性质的全面了解和推进浅水波方程在物理学等方面的应用。

The purpose of this project is to study three model equations arising from shallow water wave theory. The first one is the modified b-family equation，another model is the generalized two-component Dullin-Gottwald-Holm system and the last one is the two-component water- wave system. The blow-up and persistence property in finite time for these models will be investigated in this project. New mathematical techniques and methods will be needed to address these problems, such as taking the advantage of weight function, constructing the new function and establishing the convolution estimates related to parameters. The implementation of the project will bring a comprehensive knowledge to the characters of the shallow water wave equations and promote the application of the shallow water wave equations in physics research.