一类带约束的二维弱奇异积分方程的解<sup>*</sup>

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一类带约束的二维弱奇异积分方程的解^*

基金项目: * 广东省自然科学基金

Department of Mechanics, South China University of Technology, Guangzhou 510641, P. R. China

摘要: 本文找出二维弱奇异第一类积分方程作用着约束方程的解p.p=p(r,θ)={2/[π²k(φ₀]}√F(r,θ)-c_*(0≤r≤r_*)其中是(s,φ)原点在M(r,θ)的局部极坐标,(r,θ)是原点在O(0,0)的总体极坐标:k和F是给出的连续函数;φ₀是一常数;F(_*,θ)=c_*(常数)是研究域Q的边界围线。所用方法可推广到三维情形。
- Radon变换 /
- Abel积分方程 /
- 函数的值域 /
- 积分中值定理 /
- 接触问题 /
- Hertz解
Abstract: In this paper, the solution of a 2-D weak singular integral equation of tire first kind subjected to constraint is found and listed p=p(r,θ)={2/[π²k(φ₀]}√F(r,θ)-c_*(0≤r≤r_*) where(s,φ)is a local polar coordhrating with orighr at M(r,θ),(r,θ)is the global polar coordinating with origin at O(0,0):k and F are given continuous functions;φ₀ and C are constant;F(r_*,θ)=c_*(const.)is the boundary contour of considering range Q. The method used can be extended to 3-D cases.
- Radon transform /
- Abel integral equation /
- range /
- theorem of integral mean value of function /
- contact problem /
- Hertz’s solution

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