Study on systems of partial differential equations applying the abstract algebra

(1)证明了对于系统上的柯西=科瓦列夫斯卡娅定理，系统类似于符号上的科瓦列夫斯基接受极点是必要的。在充分性上，我们已经在一些模型上成功地证明了它，但为了处理一般情况，我们还需要对范式进行改进。(2)对于系数只依赖于时间变量的系统，强双曲性的充要条件是系统是一致可对角化的双曲Fuchsian函数。(3)p-抛物型方程组在新定义下的研究并不理想。

(1) We have shown that, for the Cauchy=Kowalevskaya theorem on a system, it is necessary that the system is similar to Kowalevskian accepting poles on symbols. On the sufficiency, we have succeeded to prove it on some models, but we need refine on the normal form in order to treat the general case. (2) On the systems with coefficients depending only on the time variable, it is necessary and sufficient for the strong hyperbolicity that the system is uniformly diagonalizable as a hyperbolic Fuchsian. (3) The study under the new definition of the p-parabolic system is not satisfactory.