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

简并抛物方程的柯西问题的适定性

• 批准号: 09640198
• 负责人: SADAMATSU Takashi
• 金额: $ 1.6万
• 依托单位: Ehime University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640198/
• 关键词: wellposedness; degenerate; microlocal analysis; Hamitonian flow; smoothing effect; propagation of the singularities; removable singularities; ratio ergodic theorem; 漸近解; 超局所解析; 正則延長; シンプレックティック変換; ポジティブトレース

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.

我们考虑偏微分方程柯西问题的适定性。Sadamatsu，T.给出了退化的一阶标准形抛物型方程适定性的一个必要条件。结果将出现在其他地方。Kajitani，K.给出了退化抛物型方程、薛定谔方程和拟线性双曲型方程适定性的一个充分条件。此外，他还讨论了薛定谔方程的光滑化性质，并明确了海尼顿流的作用是重要的。研究了复域上的柯西问题，给出了奇点传播的一个性质。Inoue，T.在一维变换的情况下证明了比率遍历定理。

项目成果

梶谷邦彦: "Quasilinear hyperbolic operators with characteristics of variable …" Tsukuba J.Math.22 1. 49-85 (1998)

Kunihiko Kajitani：“具有变量特征的拟线性双曲算子” Tsukuba J.Math.22 1. 49-85 (1998)

井上友喜: "Sojourn times in small neighborhoods of indifferent fixed points …" Ergodic Theory and Dynamical Systems.発表予定.

Yuki Inoue：“在无关紧要的固定点的小邻域中停留时间……” 遍历理论和动力系统计划进行演示。

井上友喜: "Sojourn times in small neighborhoods of indifferent fixed points ・・・" Ergodic Theory and Dynamical Systems.発表予定.

Yuki Inoue：“在无关紧要的固定点的小邻域中的逗留时间…”遍历理论和动力系统。即将呈现。

梶谷邦彦: "The Cauchy problem for degenerate parabolic equations in Gevrey …" Analli della Scuola Normale Superiore di Pisa. 16 2. 383-406 (1998)

Kunihiko Kajitani：“Gevrey 中简并抛物线方程的柯西问题……”Analli della Scuola Normale di Pisa。 16 2. 383-406 (1998)

猪狩勝寿: "Propagation of singurarities in the ramified Cauchy problem for ・・・" Publ.Res.Inst.Math.Sci.発表予定.

Katsutoshi Ikari：“分支柯西问题中奇点的传播......”Publ.Res.Inst.Math.Sci 计划演示。