Functional analytic study on global structures of nonlinear fields

非线性场整体结构的泛函分析研究

• 批准号: 09304012
• 负责人: OZAWA Tohru
• 金额: $ 14.98万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A).
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304012/
• 关键词: Nonlinear wave equations; Nonlinear Klein-Gordon equations; Nonlinear Schrodinger equations; Nonlinear scattering theory; Regularity of solutions; 非線型クライン・ゴルドン方程式; 非線型散乱; 非線型Klein-Gordon方程式; 非線型Schrodinger方程式; Harkree方程式

Mathematical reality and mechanism is studied on the nonlinear classical fields such as those described by nonlinear wave equations, nonlinear Klein-Gordon equations, and nonlinear Schrodinger equations. Special attention is given to global theories which are beyond the scope of available general theories. Small data scattering is proved for the above equations in the Sobolev spaces of any nonnegative order by specifying the associated critical nonlinearities. Large time behavior and regularity of solutions is also studied.

研究了非线性经典场的数学实在性和数学机制，如非线性波动方程、非线性Klein-Gordon方程和非线性薛定谔方程所描述的非线性经典场。特别注意的是全球性的理论，超出了现有的一般理论的范围。通过指定相关的临界非线性，证明了上述方程在任意非负阶Sobolev空间中的小数据散射。研究了解的大时间性态和正则性。

项目成果

M.Nakamura,: "The Cauchy problem for nonlinear Klein-Gordon equations in the Sobolev spaces"Publications of RIMS, Kyto University. (印刷中). (2000)

M. Nakamura，：“Sobolev 空间中非线性 Klein-Gordon 方程的柯西问题”，RIMS，京都大学（2000 年出版）。

M, Nakamura,: "The Cauchy problem for nonlinear Klein-Gordon equations in the Sobolev spaces"Publications of RIMS, Kyoto University. (印刷中). (2000)

M，Nakamura，：“Sobolev 空间中非线性 Klein-Gordon 方程的柯西问题”，京都大学 RIMS 出版物（2000 年出版）。

M. Nakamura: "Global solutions in the critical Sobolev space of the wave equations with nonlinearity of exponential growth"Mathematische Zeitschrift. 231. 479-487 (1999)

M. Nakamura：“具有指数增长非线性的波动方程临界 Sobolev 空间中的全局解”Mathematische Zeitschrift。

T.Ozawa: "Space-time estimates for null gauge forms and nonlinear Schrodinger equations" Differential and Integral Equations. 11. 201-222 (1998)

T.Ozawa：“零规范形式和非线性薛定谔方程的时空估计”微分方程和积分方程。

N.Hayashi: "Scattering theory for Hakree equation" SIAM Journal on Mathematical Analysis. 29. 1256-1267 (1998)

N.Hayashi：“Hakree 方程的散射理论”SIAM 数学分析杂志。