Analysis of the solution structure of non-linear partial differential equations corresponding to the wave phenomena and plasma phenomena

波动现象和等离子体现象对应的非线性偏微分方程的解结构分析

• 批准号: 21540186
• 负责人: ONO KOSUKE
• 金额: $ 2.75万
• 依托单位: The University of Tokushima
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540186/
• 关键词: 準線形退化型波動方程式; 非線形偏微分方程式; dissipative wave; decay rate; Vlasov-Poisson system

I conducted a study of mathematics relating to non-linear dissipative wave equations describing wave phenomena and Vlasov type equations describing plasma phenomena. I summarized the results of this research as academic papers and I published in magazines at home and abroad.For example, I got the results on the existence and uniqueness of global solutions and the asymptotic behaviors from the top and bottom of the solutions for degenerate quasi-linear hyperbolic partial differential equations to the initial boundary value problem. Further, I investigated on the conditions of the wave coefficient and the initial data for obtaining the results.

我进行了数学研究有关的非线性耗散波方程描述波现象和弗拉索夫型方程描述等离子体现象。我将这方面的研究成果归纳为学术论文并发表在国内外的杂志上，例如，我得到了退化拟线性双曲型偏微分方程整体解的存在唯一性以及从解的顶底到初边值问题的渐近性态的结果.此外，我调查的条件下的波系数和初始数据获得的结果。

项目成果

On decay estimates for some degenerate nonlinear Kirchhoff strings with dissipation

关于一些具有耗散的简并非线性基尔霍夫弦的衰减估计

• 发表时间: 2013
• 作者: R.Fukushima;N.Ueki;M.Nakanishi ; T.Suzuki;稲生啓行;小野公輔
• 通讯作者: 小野公輔

On decay properties of solutions for the Vlasov--Poisson system

弗拉索夫-泊松系统解的衰变性质

• 发表时间: 2009
• 期刊: J. Math. Tokushima Univ
• 作者: 岩塚明;島田伸一;峯拓矢;M.Kisaka;T. Suzuki;M. S. Moslehian;小野公輔;Naomasa Ueki;Yoshihiro Mizuta;S. S. Dragomir;M. Nakanishi & T. Suzuki;伊藤宏;永井敏隆;木坂正史;M. Nakamura and K. Tsutaya;Ryoki Fukushima and Naomasa Ueki;Kosuke Ono
• 通讯作者: Kosuke Ono

Global existence and decay properties of solutions for coupled degenerate dissipative hyperbolic systems of Kirchhoff type

基尔霍夫型耦合简并耗散双曲系统解的整体存在性和衰变性质

• 发表时间: 2014
• 期刊: FUNKCIALAJ EKVACIOJ
• 作者: Y. Mizuta;T. Ohno;T. Shimomura;Kosuke Ono
• 通讯作者: Kosuke Ono

A lower decay estimate for a degenerate Kirchhoff type wave equation with strong dissipation

强耗散简并基尔霍夫型波动方程的较低衰减估计

• 发表时间: 2010
• 期刊: J. Math. Tokushima Univ
• 作者: Y. Mizuta;T. Shimomura and T. Sobukawa;H. Uchizono and T. Wada;稲生啓行;小野公輔;M. Uchiyama;野村祐司;井上順子;T. Suzuki;T. Ono;Naomasa Ueki;T. Wada;永井敏隆;Kosuke Ono
• 通讯作者: Kosuke Ono

Global Existence and Decay Estimates of Solutions for Mildly Degenerate Dissipative Wave Equations of Kirchhoff Type

基尔霍夫型轻度简并耗散波方程解的全局存在与衰变估计

• 发表时间: 2011
• 作者: Yoshimi Saito;Tomio Umeda;木坂正史;Naomasa Ueki;Y. Mizuta;W. Bauer-K. Furutani-C. Iwasaki;小野公輔
• 通讯作者: 小野公輔