STRACTURE OF PARTIAL DIFFERENTIAL EQUATIONS BY SMOOTHING EFFECT

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Head investigator has organized with collaboration of investigators Symposiums and Seminars to take a direct discussion with the researcher of the university outside the country and to collect new information about the smoothing effect of dispersion equations and the regularity and the decay estimates of solutions of the Cauchy problem.. The most part of the expenses was used as the traveling expenses of the lecturer of Tsukuba seminar of analysis and of Tsukuba research meeting and Matsuyama symposium. For example, the lecturers are K. Mochizuki professor of Tokyo metropolitan university, K.Masuda professor of Tohoku University, A. Inoue Professor of T.I.T, M. Ootani Professor of Waseda University and moreover S.Spagnolo, F.Colombini both Italian professors of Pisa University, J.Vaillant Professor of University Paris 6, M.Reissig, German Professor Freiberg University etc. In this project we can analyze a Schrodinger equation with variable coefficients of second order. Though it was hardly to analyze the dispersion type equation with variable coefficients of higher order, we can begin to study and can get the results about the smoothing effects and welt posedness of the Cauchy problem by the cooperation with Wakabayashi and Igari. Kajitani and Wakabayashi got a result for Schrodinger equations with variable coefficients of second order