具有对数型奇性核的I类积分方程解

Solution of Type Ⅰ integral equation with weak singular kernel of logarithm function

在变形固体相互作用的问题中,某些物理量之间的关系确定,经常被转化为积分方程的数学表达.对于具有对数函数弱奇异性积分核的Fredholm型I类积分方程,解的性质主要取决于方程中已知函数的形式.本文推得了当已知函数为常数和幂函数时该积分方程的分析解,并且讨论了该解在定义域端点处的奇异特性.

In the interaction problem of different parts of solid, the relation of some physics factors′ determining is often transformed to the mathematics expression of integral equation. The character of the solution depends on the known function of integral equation, as to the Type Ⅰ Fredholm integral equation with logarithm function singular integral kernel. For the known functions to be constant and power function, the equation solutions are deduced. And the singular analysis of solution is also presented if the variable is approaching two extremities of determine field.