The well-posedness of the Cauchy problems for degenerate parabolic eqations

我们研究偏微分方程的柯西问题的适定性。Sadamatsu, t .给出了退化（in x）正则型一阶抛物方程的适定性的一个必要条件。结果将出现在其他地方。Kajitani, k .给出了退化抛物型方程、薛定谔型方程和拟线性双曲型方程的适定性的充分条件。进一步处理了薛定谔方程的平滑效应性质，明确了海流的重要作用。IgariK。处理了复域上的柯西问题，给出了关于奇点传播的一个性质。在一维变换的情况下，证明了比率遍历定理。

We are concerned with the wellposedness of the Cauchy problem for partial differential equations. Sadamatsu, T.gave a necessary condition of the wellposedness for degenerate (in x) 1st order parabolic equations of the canonical form. The result will be appeared elsewhere. Kajitani, K.gave a sufficient condition of the wellposedness for degenerate (in t) parabolic equations, Schrodinger type equations and quasilinear hyperbolic equations. Further he treated the smoothing effect property for Schrodinger equation and he cleared the role of Hainitonian flow is important. IgariK.treated the Cauchy problem in the complex domain and gave a Property concerning the propagation of the singularities. lnoue, T.proved the ratio ergodic theorem in the case of one-dimentional transformation.