Research on the Navier-Stokes equation and the related topics on the nonlinear differential equations
纳维-斯托克斯方程及非线性微分方程相关课题的研究
基本信息
- 批准号:15540215
- 负责人:
- 金额:$ 1.22万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2003
- 资助国家:日本
- 起止时间:2003 至 2005
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Masuda considered the discrete Lax pair for discrete Toda equation. Flashka developed the inverse scattering method for the solution of the Toda equation. On the other hand, Hirota proposed time-discrete Toda equation. Hirota-Tsujimoto-Imai constructed the disrete Lax pair. But this Lax pair does not have symmery property. Masuda constructed symmetric discrete Lax pair in the frame work of funcitonal analysis.Masuda considered the degenerate nonlinear parabolic equation of the porous medium type and showed the comparison porperty for solutions of the degenerate nonlinear parabolic equations.Morimoto considered a steady Navier-Stokes equations on a 2-D bounded domain, symmetric with respect to the y-axis. The boundary has several connected components, intersecting the y-axis. The boundary value is symmetric with respect to the y-axis satisfying the general outflow condition. The existence of the symmetric solution to the steady Navier-Stokes equations was established by Amick and Fujita. Fujita proved a key lemma concerning the solenoidal extension of the boundary value by virtual method. Morimoto gave a proof by a method different from Fujita.Ishimura considered Eguchi-Oki-Matsumura equations which describes the dynamics of pattern formation that arises from phase separation in some binary alloys. The model extends the well-known Cahn-Hilliard equation and consists of coupled two functions ; one is the local concentration and the other is the local degree of order. Ishimura showed the existence of a solutions, its symptotic profile, and in part the structure of steady state solutions.Ishimura deals with the exact solutions for stagnation flows with slip/ The problem becomes the solvability of certain third-order differential equations(ODEs). Reducing the order of ODEs, Ishimura exhibit another elementary proof of the existence and asymptotic behavior of solutions.
增田考虑离散户田方程的离散Lax对。Flashka发展了逆散射方法来求解户田方程。另一方面,Hirota提出了时间离散的户田方程。Hirota-Tsujimoto-Imai构造了离散Lax对。但这个Lax对不具有对称性。增田在泛函分析的框架下构造了对称离散Lax对,增田考虑了多孔介质型退化非线性抛物方程,并证明了退化非线性抛物方程解的比较性质,森本敏考虑了二维有界区域上关于y轴对称的定常Navier-Stokes方程.边界有几个连接的组件,与y轴相交。边界值关于y轴对称,满足一般流出条件。Amick和Fujita建立了定常Navier-Stokes方程对称解的存在性。Fujita用虚方法证明了关于边值螺线管延拓的一个关键引理。Morimoto用不同于Fujita的方法给出了证明。Ishimura考虑了描述某些二元合金中由相分离引起的图案形成动力学的Eguchi-Oki-Matsumura方程。该模型扩展了著名的Cahn-Hilliard方程,并由耦合的两个功能,一个是本地浓度和其他的是本地的程度的顺序。石村表明存在的解决方案,其渐近的配置文件,并在部分结构的稳定状态solutions.Ishimura处理的确切解决方案停滞流滑移/问题成为可解性的某些三阶微分方程(常微分方程)。通过降低常微分方程的阶数,Ishimura给出了解的存在性和渐近性的另一个初等证明。
项目成果
期刊论文数量(48)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Singular perturbation problem for steady state solutins to a model equation of phase separation
相分离模型方程稳态解的奇异摄动问题
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:増田 久弥;N.Ishimura;N.Ishimura
- 通讯作者:N.Ishimura
An elementary approach to the analysis of exact solutions for the Navier-Stokes stagnation flows flows with slips
分析带滑移的纳维-斯托克斯停滞流精确解的基本方法
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:N.Ishimura;T.K.Ushijima
- 通讯作者:T.K.Ushijima
Singular perturbation problem for steady state solutions to a model equation of phase separation
- DOI:10.1002/zamm.200410216
- 发表时间:2005-12
- 期刊:
- 影响因子:0
- 作者:T. Hanada;N. Ishimura;M. Nakamura
- 通讯作者:T. Hanada;N. Ishimura;M. Nakamura
A remark on the existence of 2-D steady Navier-Stokes flow in symmetric domain under general outflow condition
一般流出条件下对称域二维稳态纳维-斯托克斯流存在性的评述
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:増田 久弥;N.Ishimura;N.Ishimura;K.Masuda;N.Ishimura;N.Ishimura;増田 久弥;Hiroko Morimoto
- 通讯作者:Hiroko Morimoto
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MASUDA Kyuya其他文献
MASUDA Kyuya的其他文献
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{{ truncateString('MASUDA Kyuya', 18)}}的其他基金
Study on Navier-Stokes equations and the related nonlinear differential equations
纳维-斯托克斯方程及相关非线性微分方程研究
- 批准号:
18540222 - 财政年份:2006
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study on Navier-Stokes equations and related nonlinear partial differential equations
纳维-斯托克斯方程及相关非线性偏微分方程研究
- 批准号:
12640223 - 财政年份:2000
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study on Navier-Stokes equations and related nonlinear partial differential equations
纳维-斯托克斯方程及相关非线性偏微分方程研究
- 批准号:
10440055 - 财政年份:1998
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Study of Nonlinear Partial Differential Equations from the View Point of Functional Analysis
从泛函分析的角度研究非线性偏微分方程
- 批准号:
01460004 - 财政年份:1989
- 资助金额:
$ 1.22万 - 项目类别:
Grant-in-Aid for General Scientific Research (B)