Nonlinear Inverse Problems and Singular Integral Equations

非线性反问题和奇异积分方程

• 批准号: 10440038
• 负责人: KAMIMURA Yutaka
• 金额: $ 4.29万
• 依托单位: Tokyo University of Fisheries
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440038/
• 关键词: nonlinear inverse problem; singular integral equation; Wiener-Hopf equation; inverse bifurcation problem; mathematical ecology; population dynamics; conductivity identification; 反応拡散方程式; Wiener-Hopf作用素; 非線型逆問題; 熱伝導率; 非線形微分方程式; 積分方程式; 非線形項

Several nonlinear inverse problems in mathematical sciences are discussed : a friction coefficient identification problem, a nonlinearity identification problem in nonlinear oscillations, a time-dependent thermal conductivity identification problem, inverse bifurcation problem in mathematical ecology (nonlinear reaction kinetics identification problem in a diffusional model of population dynamics from the relation between growth rates and certain central densities of population distributions). A certain class of singular integral equations plays a principal role in our mathematical analysis of the inverse problems ; some existence results of the solutions to the integral equations are established and applied to the inverse problems.

讨论了数学科学中的几个非线性反问题：摩擦系数识别问题，非线性振动中的非线性识别问题，时间相关热导率识别问题，数学生态学中逆分歧问题（非线性反应动力学识别问题的扩散模型的人口动力学之间的关系增长率和人口分布的某些中心密度）。一类奇异积分方程在反问题的数学分析中起着重要的作用，建立了这类积分方程解的存在性结果，并将其应用于反问题。

项目成果

Y.Kamimura: "Anti-Abel Integral equation and inverse problems"数理解析研究所講究録. 印刷中. (2000)

Y. Kamimura：“反阿贝尔积分方程和反问题”数学科学研究所出版（2000）。

Yutaka Kamimura: "Uniqueness of the nonlinear term of a boundary value problem from the first bifurcating branch" Proc.Japan Acad.Ser.A. 74. 53-56 (1998)

Yutaka Kamimura：“来自第一分叉分支的边值问题的非线性项的唯一性”Proc.Japan Acad.Ser.A。

K.Iwasaki, Y.Kamimura: "Inverae bifurcation problem, a survey of recent results"Biomathematics, Bioinformatics, and Applications of Functional Differential Difference Equations. 104-113 (2000)

K.Iwasaki、Y.Kamimura：“Inverae 分岔问题，最近结果的调查”生物数学、生物信息学和函数微分差分方程的应用。

K. Iwasaki and Y. Kamimura: "Inverse bifurcation problem, singular Wiener-Hopf equations, and mathematical models in ecology"J. Math. Biol.. 43. 101-143 (2001)

K. Iwasaki 和 Y. Kamimura：“逆分岔问题、奇异 Wiener-Hopf 方程和生态学数学模型”J.

K.Iwasaki and Y.Kamimura: "Inverse bifurcation problem, singular Wiener-Hopf equations, and mathematical models in ecology"J.Math.Biology. (to appear).

K.Iwasaki 和 Y.Kamimura：“逆分岔问题、奇异 Wiener-Hopf 方程和生态学数学模型”J.Math.Biology。