Smoothing effect of Partial differential equations

偏微分方程的平滑效果

• 批准号: 11440038
• 负责人: KUNIKIKO Kajitani
• 金额: $ 7.74万
• 依托单位: Tsukuba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440038/
• 关键词: smoothing effect; Schrodinger equation; dispersion equation; regularity; Gevrey class; Cauchy problem; smoothing effect; Schrodinger方程式; 平滑化効果; シュレヂンガー方程式; 双曲型方程式; 退任放物型方程式

In the case of coefficients depending on time and places the problem of smoothing effect was considered to be very difficult technically. In this study we can find the new method to overcome this difficulty and are able to treat the more general dispersion equations. The results obtained in this study was published in the symposiums in Japan and in the international conference.In particular it is a great progress to be able to prove the analytically smoothing effect of general dispersion equations.

在系数随时间和地点变化的情况下，平滑效果的问题被认为是非常困难的技术问题。在本研究中，我们可以找到新的方法来克服这一困难，并能够处理更一般的色散方程。本研究的结果发表在日本的学术研讨会和国际会议上。特别是能够证明一般色散方程的解析平滑效应是一个很大的进步。

项目成果

H.Takamura: "The lift span of classical solution to systems of nonlinear wave equation"Rend.Inst.Math.Oniv Trieste XXXI. 225-243 (2000)

H.Takamura：“非线性波动方程组经典解的升力跨度”Rend.Inst.Math.Oniv Trieste XXXI。

S.Poi: "Smoothing effect for Schrodinger equations and slabal be havior of seodesic flow"Math.Ann.. 318. 355-389 (2000)

S.Poi：“薛定谔方程的平滑效应和沉降流的平板行为”Math.Ann.. 318. 355-389 (2000)

高村博之: "The lifespan of classical solutions to systems of Nonlinear wave equation"Rend, Istit, Mat. Univ.Trieste. XXXI. 225-243 (2000)

Hiroyuki Takamura：“非线性波动方程系统的经典解的寿命”Rend，Istit，Mat.Trieste 225-243（2000）。

梶谷邦彦: "Propagation of analy.ticity of the solutions to the Cauchy problem"Ann.Scuola Norm, Sup.Pisa. 28. 471-487 (1999)

Kunihiko Kajitani：“柯西问题解的分析性传播”Ann.Scuola Norm，Sup.Pisa 28. 471-487 (1999)

K.Kajitani: "Propagation of analyticity of the solution of systems"Ann.Scuola Norm.Sup Pisa. 28. 471-487 (1999)

K.Kajitani：“系统解的分析性传播”Ann.Scuola Norm.Sup Pisa。