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

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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.