STRACTURE OF PARTIAL DIFFERENTIAL EQUATIONS BY SMOOTHING EFFECT

基于平滑效应的偏微分方程的结构

• 批准号: 13440040
• 负责人: KAJITANI Kunihiko
• 金额: $ 5.12万
• 依托单位: UNIVERSITY OF TSUKUBA
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440040/
• 关键词: Dispersion equation; mocrolocal smoothing effect; global solution of nonlinear problem; Schrodinger equation; regularity of solution; time decay; 非線形問題の大域解; Smoothing effect; Schrodinger equation; Dispersion; Micro local analysis; Differential

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

首席研究员与研究人员合作组织了研讨会和研讨会，与国外大学的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规律性和衰减估计的新信息。大部分费用用于筑波分析研讨会讲师的差旅费，以及筑波研究会议和松山研讨会讲师的差旅费。例如，主讲人有东京都大学望月教授、东北大学增田教授、东京工业大学井上教授、早稻田大学Ootani教授、意大利比萨大学教授S.Spagnolo、F.Colombini、巴黎第六大学教授J.Vaillant、德国弗莱堡大学教授M. reissig等。在这个项目中，我们可以分析一个二阶变系数薛定谔方程。虽然很难分析高阶变系数色散型方程，但通过与Wakabayashi和Igari的合作，我们可以开始研究并得到关于柯西问题的平滑效果和良态性的结果。Kajitani和Wakabayashi得到了二阶变系数薛定谔方程的结果

项目成果

梶谷邦彦: "The Cauchy problem for hyperbolic operators dominated by time function"A Dekker Series of Lecture Notes in Pure and Applied Mathematics. 233. 260-285 (2003)

Kunihiko Kajitani：“由时间函数支配的双曲算子的柯西问题”德克纯粹与应用数学讲座系列 233. 260-285 (2003)

K.Kajitani, S.Spagnolo: "Strong Gevrey solrability for a system of L. P. D. O"Progress in Nonlinear D. E. and Aplications. 52. 121-142 (2002)

K.Kajitani、S.Spagnolo：“L.P.D.O 系统的强 Gevrey 可解性”非线性 D.E. 和应用的进展。

梶谷邦彦: "Smoothing effect in Gevrey classes for Schrodinger equations I"A Dekker Series of Lecture Notes in Pure and Applied Mathematics. 233. 31-40 (2003)

Kunihiko Kajitani：“薛定谔方程 I 的 Gevrey 类中的平滑效应”Dekker 纯粹数学和应用数学讲座系列 233. 31-40 (2003)

田村英夫: "Magnetic scattering at low energy"Nagoya Math. J.. 155. 95-151 (1999)

田村秀夫：“低能量磁散射”名古屋数学杂志 155. 95-151 (1999)

K.KAJITANI: "Smoothing effect in Gevrey classes for Schrodinger equations"A Dekker Series of Lecture Note in Pure and Appl.Math.. 233. 269-286 (2003)

K.KAJITANI：“薛定谔方程的 Gevrey 类中的平滑效应”A Dekker Series of Lecture Note in Pure and Appl.Math.. 233. 269-286 (2003)