偏微分方程的控制问题在物理、力学以及水利工程等方面具有很强的应用背景，属于近代应用数学研究中一个十分活跃的前沿研究方向。关于偏微分方程控制问题的理论研究，虽已有很多结果，但由于实际问题的复杂性和多样性，相应的研究往往有较大的难度，在数学上是一个挑战，而另一方面，结合实际模型进行深入透彻的研究，可望更好地解释现象的本质，得到深入的结果。.当不考虑渠道的摩擦影响且假设渠道底部是平面时，Saint-Venant方程的稳定性已有相对完整的结果，但现实中，渠道的摩擦影响是不能忽略的，且渠道底部一般都有坡度，本课题拟研究将这两个因素加入后带有非线性源项的Saint-Venant方程的稳定性。. 对Korteweg-de Vries方程，拟研究较少控制下的能控性及稳定性问题。此时，能控性及稳定性问题的研究与水渠的长度紧密相关，本课题将重点研究水渠长度属于临界集合的这一尚未解决的困难情形。

Control problems for partial differential equations are very popular due to its widely applications in physics, mechanics and hydraulic system. There are already many classical results for theoretically study of control problems related to partial differential equations. However, it is still a challenge to apply these results to reality due to the complexity and variety of the real world. On the other hand, it would be very helpful if we could study the models thoroughly and provide essential results through the phenomena. . In the case where we ignore the influences of the friction and slope, the results concerning the stabilization of Saint-Venant equation is relatively complete. However, usually, these two factors can not be ignored in reality. We take these two factors into consideration and mainly study the sabilization of Saint-Venant equation with nonlinear source term.. For Korteweg-de Vries equations, we study the corresponding controllability and stabilization problems with less controls. When using less controls, the study of controllability and stabilization has great relationship with the length of the channel. We will mainly consider the open problem in the case where the length belongs to the critical set in this proposal.