STRACTURE OF PARTIAL DIFFERENTIAL EQUATIONS BY SMOOTHING EFFECT

首席调查员与调查人员合作组织了研讨会和研讨会，与国外的大学研究人员进行了直接讨论，并收集了关于色散方程的平滑效应和柯西问题解的正则性和衰减估计的新信息。大部分费用被用作筑波分析研讨会和筑波研究会议和松山研讨会的讲师的旅费。例如，讲师有东京都大学教授K.Mochizuki，东北大学教授K.Masuda，东京工业大学的A.Inoue教授，早稻田大学的M.Ootani教授，以及比萨大学的意大利教授S.Spagnolo，F.Columbini，巴黎大学的J.Vaillant教授，德国弗莱伯格大学的M.Reissig教授等。虽然分析高阶变系数的色散型方程很难，但我们可以通过与Wakabayashi和Igari的合作，开始研究和得到柯西问题的光滑化效应和正则性的结果。Kajitani和Wakabayashi得到了二阶变系数薛定谔方程的一个结果

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