An Inverse Bifurcation Problem and a generelization of Abel's equation
逆分岔问题和阿贝尔方程的推广
基本信息
- 批准号:07640179
- 负责人:
- 金额:$ 1.28万
- 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:1995
- 资助国家:日本
- 起止时间:1995 至 1997
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research was intended to solve the following problem :Problem 1 (Inverse Bifurcation Problem). Determine a nonlinear term f of the boundary value problem=u''+ [lambda-q (x)] u=f (u), 0<less than or equal>x<less than or equal>pi/2, '=d/u' (0) =u (pi/2) =0.from its first bifurcating branch.It was also a purpose of this research to find what kind of integral equation appears when we try to solve the inverse bifurcation problem.Concerning Problem 1, two results have been established : a local existence result and a uniqueness result. In the course of our research we have realized that our method used for obtaining the above results is effective in solving similar inverse problems of determining unknown nonlinear terms appearing in boundary value problems from information on their spectral parameters. Foremost among those is the following problem :Problem 2 (Denisov-Lorenzi Problem). Given functions a (lambda), b (lambda) on the interval [0, A], determine a nonlinear term g, with which the (overdetermined) boundary value problem=u''=lambdag (u), 0<x<1, '=d/u (0) =1, u' (0) =a (lambda), u (1) =b (lambda)admits a solution u for each lambda [0, A].This problem has been discussed and an improvement of the local existence theorem in the work is given. We have also given an answer to the question : what kind of integral equations appear in establishing local existence results for Problems 1 and 2. A class of integral equations treated there would enable us to present a basic aspect of integral equations arising from nonlinear inverse problems.
本研究主要解决以下问题:问题1(逆分叉问题)。从第一个分支分支出发,确定了边值问题= u“+ [xda-q(x)] u=f(u),0 <less than or equal>x <less than or equal>pi/2,”=d/u“(0)=u(pi/2)= 0.的一个非线性项f,并研究了在解逆分支问题时,会出现什么样的积分方程.对于问题1,得到了两个结果:局部存在性结果和唯一性结果.在我们的研究过程中,我们已经意识到,我们的方法用于获得上述结果是有效的,在解决类似的反问题,确定未知的非线性项出现在边值问题,从他们的谱参数的信息。问题2(Denisov-Lorenzi问题)。给定区间[0,A]上的函数a(lambda)、B(lambda),确定非线性项g,利用该非线性项g(超定)边值问题= u“= dag(u),0<x<1,”=d/u(0)=1,u“(0)=a(lambda),u(1)=B(lambda)对于每个lambda [0,本文讨论了这一问题,并改进了文[1]中的局部存在定理。我们还回答了问题1和问题2的局部存在性结果的建立过程中会出现什么样的积分方程。一类积分方程的治疗有将使我们能够提出一个基本方面的积分方程所产生的非线性反问题。
项目成果
期刊论文数量(6)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Y.Kamimura: "An inverse problem in bifurcation theory,III" Proceedings of American Mathematical Society. 123. 3051-3056 (1995)
Y.Kamimura:“分叉理论中的反问题,III”美国数学会论文集。
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- 影响因子:0
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Yutaka Kamimura: "An inverge problem of determining a nonlinear term in ordinary differential equation" Differential and Integral Equations. (未定).
Yutaka Kamimura:“确定常微分方程中非线性项的倒数问题”微分和积分方程(待定)。
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- 影响因子:0
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Y.Kamimura: "An inverse problem in bifurcation theory, III" Proc.Amer.Math.Soc.123. 3051-3056 (1995)
Y.Kamimura:“分岔理论中的反问题,III”Proc.Amer.Math.Soc.123。
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- 影响因子:0
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K.Iwasaki and Y.Kamimura: "An inverse bifurcation problem and an integral equation of the Abel type" Inverse Problems. 13. 1015-1031 (1997)
K.Iwasaki 和 Y.Kamimura:“反分岔问题和阿贝尔型积分方程”反问题。
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- 影响因子:0
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Y.Kamimura: "Uniquenes of the norlinear term of a bounday value problem from the first bifurcati branch" Proceedings of the Japan Academy. (印刷中).
Y. Kamimura:“第一分叉分支的体值问题的非线性项的独特性”日本学院学报(正在出版)。
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KAMIMURA Yutaka其他文献
KAMIMURA Yutaka的其他文献
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{{ truncateString('KAMIMURA Yutaka', 18)}}的其他基金
Inverse problems and nonlinear integral transforms
反问题和非线性积分变换
- 批准号:
21540165 - 财政年份:2009
- 资助金额:
$ 1.28万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Inverse Problems in Nonlinear Phenomena
非线性现象中的反问题
- 批准号:
15540201 - 财政年份:2003
- 资助金额:
$ 1.28万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Nonlinear Inverse Problems and Singular Integral Equations
非线性反问题和奇异积分方程
- 批准号:
10440038 - 财政年份:1998
- 资助金额:
$ 1.28万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
相似海外基金
The determination of the nonlinear term by the bifurcating curve of a solution of a nonlinear boundary valne problem
非线性边值问题解的分叉曲线确定非线性项
- 批准号:
05640157 - 财政年份:1993
- 资助金额:
$ 1.28万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)