High frequency asymptotic analysis for nonlinear PDEs of hyperbolic and dispersive type

双曲型和色散型非线性偏微分方程的高频渐近分析

• 批准号: 22740089
• 负责人: SUNAGAWA Hideaki
• 金额: $ 2.08万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22740089/
• 关键词: 漸近解析; 非線形波動; シュレディンガー方程式; 波動方程式; クライン・ゴルドン方程式

Nonlinear partial differential equations of hyperbolic and dispersive type are studied from the view point of high frequency asymptotic analysis. Relations between the null structure and resonant interactions are revealed for systems of nonlinear Klein-Gordon equations. Examples on small data blow-up for nonlinear Schrodinger equations are constructed, and estimates for the order of the lifespan of the blowing-up solutions are provided. The method of high frequency asymptotics are also applied to a class of nonlinear wave equations not satisfying the null condition.

从高频渐近分析的观点研究了非线性双曲型色散型偏微分方程。揭示了非线性Klein-Gordon方程组的零结构与共振相互作用之间的关系。构造了非线性薛定谔方程小数据爆破的例子，并给出了爆破解寿命的阶数估计。将高频渐近方法应用于一类不满足零条件的非线性波动方程。

项目成果

Quadratic nonlinear Schrodinger systems in the presence of mass resonance

存在质量共振的二次非线性薛定谔系统

• 发表时间: 2012
• 作者: Y.Kagei;Y.Maekawa;Kazuhiro Takimoto;砂川秀明;Kazumasa Kuwada;Yasunori Maekawa;K. Kuwada;滝本和広;砂川秀明
• 通讯作者: 砂川秀明

A remark on the algebraic normal form method applied tothe Dirac-Klein- Gordon system in twospace dimensions

二维Dirac-Klein-Gordon系统中代数范式方法的评述

• 发表时间: 2012
• 期刊: RIMS Kokyuroku Bessatsu
• 作者: M. Ikeda;A. Shimomura and H.Sunagawa
• 通讯作者: A. Shimomura and H.Sunagawa

On quadratic nonlinear Klein-Gordon systems in twospace dimensions

双空间维度二次非线性克莱因-戈登系统

• 发表时间: 2011
• 作者: Gallay;Th. and Maekawa;Y.;H.Sunagawa
• 通讯作者: H.Sunagawa

The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions

• DOI: 10.1007/s00028-012-0160-4
• 发表时间: 2012-07
• 期刊: Journal of Evolution Equations
• 影响因子: 1.4
• 作者: S. Katayama;Daisuke Murotani;Hideaki Sunagawa

A note on the null condition for quadratic nonlinear Klein‐Gordon systems in two space dimensions

• DOI: 10.1002/cpa.21392
• 发表时间: 2011-05
• 期刊: Communications on Pure and Applied Mathematics
• 影响因子: 3
• 作者: S. Katayama;T. Ozawa;Hideaki Sunagawa