Global solution structure and the stability of nonlocal nonlinear second order boundary value problems with definite integrals

非局部非线性二阶定积分边值问题的全局解结构与稳定性

基本信息

  • 批准号:
    15540220
  • 负责人:
  • 金额:
    $ 2.3万
  • 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

项目摘要

First, Lou-Ni-Yotsutani [DCDS 2004] investigated a limiting equation to a cross-diffusion equation that appears in mathematical biology. We showed that it has different kinds of singular solutions and revealed the structure of all solutions.This problem is a nonlocal nonlinear elliptic boundary problem, for which no method was known to solve it. We discovered a new method, which are the combination of the modern method of PDE and classical analysis and algebra.There are a lot of interesting problems for which our method is applicable.A problem of the Oseen's spiral flow is one of them, for which we obtained the complete bifurcation diagram in Ikeda-Kondo-Okamoto-Yotsutani [CPAA 2003].Matsumoto-Murai-Yotsutani [Pisa, 2005] gave the complete answer for a problem to determine curves with the least energy under the given length.Second, Kosugi-Morita-Yotsutani [CPAA 2005, J.Math.Phy. 2005] have revealed the complete Global bifurcation branches one dimensional Ginzburg-Landau equations with periodic boundary conditions.
首先,Lou-Ni-Yotsutani [DCDS 2004]研究了数学生物学中出现的交叉扩散方程的极限方程。我们证明了该问题具有不同类型的奇异解,并揭示了所有解的结构.该问题是一个非局部非线性椭圆边值问题,目前还没有一种求解方法.我们发现了一种新的方法,它是现代偏微分方程方法与经典分析和代数方法的结合,有许多有趣的问题是我们的方法所适用的. Oseen螺旋流问题在Ikeda-Kondo-Okamoto-Yotsutani [CPAA 2003]中我们得到了完全的分岔图,Matsumoto-Murai-Yotsutani [比萨,2005]给出了在给定长度下确定具有最小能量的曲线问题的完全答案。2005]揭示了具有周期边界条件的一维Ginzburg-Landau方程的完全全局分支。

项目成果

期刊论文数量(56)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On a limiting system in the Lotka-Volterra competition with cross-diffusion,
关于具有交叉扩散的 Lotka-Volterra 竞争的限制系统,
Global bifurcation structure of a one-dimensional Ginzburg-Landau model
一维 Ginzburg-Landau 模型的全局分叉结构
  • DOI:
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    0
  • 作者:
    S.Kosugi;S.Kosugi;S.Kosugi;S.Kosugi
  • 通讯作者:
    S.Kosugi
Existence and global stability of traveling curved front in the Allen-Cahn equations
Allen-Cahn 方程中行进曲锋的存在性及其全局稳定性
E.Yanagida, S.Yotsutani: "Recent Topics on Nonlinear Partial Differential Equations : Structure of Radial Solutions for Semilinear Elliptic Equations"Amer.Math.Soc.Transl., Series : Selected Papers on Analysis and Differential Equations. 2・211. 121-137 (2
E.Yanagida、S.Yotsutani:“非线性偏微分方程的最新主题:半线性椭圆方程的径向解的结构”Amer.Math.Soc.Transl.,系列:分析和微分方程论文选集 2·211。 -137(2
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
J.-S.Guo, Y.Morita: "Entire solutions of reation-diffusion equations and an application to discrete diffusive equations"Discrete and Continuous Dynamical Systems. to appear. (2004)
J.-S.Guo,Y.Morita:“反应扩散方程的完整解及其在离散扩散方程中的应用”离散和连续动力系统。
  • DOI:
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  • 影响因子:
    0
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YOTSUTANI Shoji其他文献

YOTSUTANI Shoji的其他文献

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{{ truncateString('YOTSUTANI Shoji', 18)}}的其他基金

Research on profiles and the global bifurcation structure by explicit representation formula using elliptic functions
利用椭圆函数显式表示公式研究轮廓和全局分叉结构
  • 批准号:
    24540221
  • 财政年份:
    2012
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Differential equations reduced to transcendental equations including complete elliptic integrals and their global solution structure
微分方程简化为超越方程,包括完全椭圆积分及其全局解结构
  • 批准号:
    21540232
  • 财政年份:
    2009
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Research on the stability and asymptotic shapes of nonlocal nonlinear boundary value problems including unknown definite integrals
含未知定积分的非局部非线性边值问题的稳定性和渐近形状研究
  • 批准号:
    18540224
  • 财政年份:
    2006
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Research on canonical forms to nonlinear elliptic boundary value problems and the global structure of all solutions including singular solutions
非线性椭圆边值问题的规范形式和包括奇异解在内的所有解的全局结构研究
  • 批准号:
    12640225
  • 财政年份:
    2000
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Resarchs on Solutions of Nonlinear Elliptic Equations and Numcrical Analysis
非线性椭圆方程解及数值分析研究
  • 批准号:
    09440087
  • 财政年份:
    1997
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
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