Studies on the sufficient conditions for the global existence of solutions to the exterior problems for nonlinear hyperbolic equations

非线性双曲方程外问题解全局存在的充分条件研究

• 批准号: 20540211
• 负责人: KATAYAMA Soichiro
• 金额: $ 1.33万
• 依托单位: Wakayama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540211/
• 关键词: 非線形波動方程式; 零条件; 大域解; 外部問題; クラインーゴルドン方程式; 双曲型方程式; 波動方程式; 非線形; クライン-ゴルドン方程式; null条件; 漸近挙動; 初期値境界値問題

We consider the exterior problem for the linear wave equations, and obtained the convergence rate of the solution to its asymptoics. As an application, we also obtained the precise lower bound estimate of the lifespan of the solutions to the exterior problem for semilinear wave equations. We investigated the asymptotic behavior of global solutions to the systems of nonlinear wave equations with multiple propagation speeds. In connection to the exterior problem, we also study the Cauchy problem in the whole space for various kinds of nonlinear systems, such as systems of wave or Klein-Gordon equations and coupled systems of these equations, and investigated the condition for the global existence of solutions and their asymptotic behavior.

考虑线性波动方程的外问题，得到了解的渐近性的收敛速度。作为应用，我们还得到了半线性波动方程外问题解的寿命的精确下界估计。研究了具有多个传播速度的非线性波动方程组整体解的渐近性。对于外问题，我们还研究了各种类型的非线性系统的柯西问题，如波动系统或Klein-Gordon方程组以及这些方程的耦合系统，并研究了整体解存在的条件及其渐近性。

项目成果

Global existence for systems of the nonlinear wave and Klein-Gordon equations in 3D

3D 非线性波系统和 Klein-Gordon 方程组的全局存在性

• 发表时间: 2009
• 作者: Yuki Nai to;Satoshi Tanaka;Marie Choda;T. Ishiwata;Yuki Naito;T.Ishiwata;木下保;Yuki Naito;木下保;片山聡一郎;梶木屋龍治;Marie Choda;T. Aiki;片山聡一郎
• 通讯作者: 片山聡一郎

Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions

三个空间维度中半线性波动方程组的渐近点行为

• 发表时间: 2010
• 作者: R.Kajikiya;Yong-Hoon Lee;Inbo Sim;浅倉邦彦,小栗栖修,真田博文,鈴木正清;Sumio Yamada;K. Anada and T. Ishiwata;片山聡一郎
• 通讯作者: 片山聡一郎

Global existence for coupled systems of nonlinear wave and Klein–Gordon equations in three space dimensions

• DOI: 10.1007/s00209-010-0808-0
• 发表时间: 2009-08
• 期刊: Mathematische Zeitschrift
• 影响因子: 0.8
• 作者: S. Katayama