The refined diagonalization procedure and a development on the evolution equations with smooth coefficients

改进的对角化过程和光滑系数演化方程的发展

• 批准号: 22540197
• 负责人: HIROSAWA Fumihiko
• 金额: $ 2.58万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540197/
• 关键词: 双曲型方程式; 変数係数; 波動方程式; 非線形波動方程式; 双曲型偏微分方程式; 偏微分方程式; 非線形

In this project, we studied evolution equations with smooth variable coefficients by using a special technique for the precise representations of the solutions, which is called "the refined diagonalization procedure". This method is very useful for the analysis of the initial values problems of hyperbolic equations with variable coefficients, for example, wave equations, Klein-Gordon type equations, second order hyperbolic equations and semi-linear wave equations. Indeed, we succeeded to prove some estimates for these problems, which couldn't be solved by using the previous method, by using our new method. Moreover, we expect that our results will be applicable for the analysis of non-linear problems, in particular, for the global solvability of Kirchhoff equation in non-realanalytic class.

在这个项目中，我们用一种特殊的技巧来研究光滑变系数发展方程的解的精确表示，这种方法被称为“精化对角化过程”。这种方法对于分析变系数双曲型方程，如波动方程、Klein-Gordon方程、二阶双曲型方程和半线性波动方程的初值问题是非常有用的。事实上，我们用我们的新方法成功地证明了这些问题的一些估计，这些估计是用以前的方法无法解决的。此外，我们期望我们的结果将适用于非线性问题的分析，特别是非实解析类中Kirchhoff方程的整体可解性。

项目成果

On energy estimates for second order hyperbolic equations with Levi conditions for higher order regularity

高阶正则性 Levi 条件下二阶双曲方程的能量估计

• DOI: 10.1007/s11565-011-0121-9
• 发表时间: 2011
• 期刊: Annali dell'Universita di Ferrara. Sezione VII Scienze Matematiche
• 作者: Fumihiko Hirosawa;Tang Bao Ngoc Bui
• 通讯作者: Tang Bao Ngoc Bui

On second order weakly hyperbolic equations and the ultradifferentiable classes

关于二阶弱双曲方程和超微类

• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: Haruhisa Ishida;Fumihiko Hirosawa
• 通讯作者: Fumihiko Hirosawa

A class of non-analytic functions for the global solvability of Kirchhoff equation

基尔霍夫方程全局可解性的一类非解析函数

• 发表时间: 2015
• 作者: Takayuki Myo;Hiroshi Toki;Kiyomi Ikeda;Hisashi Horiuchi;Tadahiro Suhara;Mengjiao Lyu;Masahiro Isaka;and Taiichi Yamada;F. Hirosawa
• 通讯作者: F. Hirosawa

On the energy estimates for second order homogeneous hyperbolic equations with Levi-type conditions

Levi型条件下二阶齐次双曲方程的能量估计

• 发表时间: 2011
• 作者: 斎藤吉助;三谷健害;小室直人;F.Hirosawa;増本誠;斎藤吉助;F.Hirosawa;田中亮太朗;幡谷泰史;廣澤史彦;田中亮太朗;増本誠;廣澤史彦;斎藤吉助;山田陽;F. Hirosawa;F. Hirosawa;Hiroshi Yanagihara;F.Hirosawa;Masakazu Shiba;F.Hirosawa
• 通讯作者: F.Hirosawa

On the global solvability for semilinear wave equations with smooth propagation speeds

传播速度光滑的半线性波动方程的全局可解性

• 发表时间: 2012
• 作者: Y.Kimura;K.Sato;Hiroya Ito;伊藤秀一;K. Kajitani;木村泰紀;石田晴久;伊藤秀一;梶谷邦彦;石田晴久;伊藤秀一;K. Kajitani;伊東裕也;伊藤 秀一;木村泰紀;Kunihiko Kajitani;廣澤史彦
• 通讯作者: 廣澤史彦