Asymptotic analysis for nonlinear dispersive and hyperbolic equations

非线性色散和双曲方程的渐近分析

• 批准号: 18740076
• 负责人: SHIMOMURA Akihiro
• 金额: $ 1.48万
• 依托单位: Tokyo Metropolitan University (2007-2008)Gakushuin University (2006)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2008
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18740076/
• 关键词: 解析学; 偏微分方程式; 関数解析; 微分方程式; 函数解析; 関数方程式論; 関数解析学; 応用数学; 応用数理

本研究課題では,長距離型非線型消散項を伴うシュレディンガー方程式の解の長時間挙動(時間減衰評価や漸近形),ゲージ不変でない非線型項を伴うシュレディンガー方程式の散乱理論,4階シュレディンガー型方程式の解の長時間挙動(終値問題),シュレディンガー改良ブシネスク方程式系の散乱理論の研究を行い,研究成果を得た。得られた研究成果は,学術雑誌(査読付)に公表した。

In this study, the long-distance non-linear dissipative equation is used to solve the long-term equation (time-dependent decay equation is closed), the non-linear project is related to the random theory of the equation, and the equation is solved for a long time (problem). In the course of the study of the theory of scatter theory, the results of the research have been improved. The research results will be reviewed, and the academic journals will be published in a public form.

项目成果

劣臨界指数の非線型消散項を伴うシュレディンガー方程式の解の漸近挙動

具有亚临界指数非线性耗散项的薛定谔方程解的渐近行为

• 发表时间: 2008
• 作者: N.;Kumano-go・D.;Fujiwara;Akihiro Shimomura;T.Suzuki;Naoto Kumano-go;T.Suzuki;Naoto Kumanogo;Naoyasu Kita;T.Suzuki;Jun-ichi Segata;Naoto Kumano-go;T.Suzuki;T.Suzuki;熊ノ郷直人;Jun-ichi Segata and Akihiro Shimomura;Akihiro Shimomura and Yoshio Tsutsumi;T.Suzuki;Naoto Kumano-go;Akihiro Shimomura;T. Suzuki;熊ノ郷直人;T. Suzuki;Akihiro Shimomura;T. Suzuki;Akihiro Shimomura;熊ノ郷直人;Naoto Kumano-go;Jun-ichi Segata;T. Suzuki;Naoto Kumano-go;鈴木 智成;下村明洋;鈴木 智成;Naoto Kumano-go;下村明洋
• 通讯作者: 下村明洋

Asymptotic behavior of solutions to Schrödinger equations with a subcritical dissipative nonlinearity

• DOI: 10.1016/j.jde.2007.07.003
• 发表时间: 2007-11
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: Naoyasu Kita;A. Shimomura

A short review of scattering for the Schrodinger-improved Boussinesq system,

对薛定谔改进的 Boussinesq 系统的散射的简短回顾，

• 发表时间: 2008
• 期刊: Hokkaido Mathematical Journal 37
• 作者: Naoto Kumano-go;Daisuke Fujiwara;T. Suzuki;Akihiro Shimomura
• 通讯作者: Akihiro Shimomura

Nonexistence of scattering states for some quadratic nonlinear Schrodinger equation in two space dimensions

二维空间中二次非线性薛定谔方程不存在散射态

• 发表时间: 2006
• 期刊: Diff. and Int. Eq 19
• 作者: A.;Shimomura;Y.;Tsutsumi
• 通讯作者: Tsutsumi

Large time behavior of solutions to Schrödinger equations with a dissipative nonlinearity for arbitrarily large initial data

• DOI: 10.2969/jmsj/06110039
• 发表时间: 2009
• 期刊: Journal of The Mathematical Society of Japan
• 影响因子: 0.7
• 作者: Naoyasu Kita;A. Shimomura