一类对偶积分方程组正则化为Cauchy奇异积分方程组解法

本文基于Mellin变换法求解复杂更一般形式的对偶积分方程组．通过积分变换，由实数域化成复数域上的方程组，引入未知函数的积分变换，移动积分路径，应用Cauchy积分定理，实现退耦正则化为Cauchy奇异积分方程组，由此给出一般性解，并严格证明了对偶积分方程组退耦正则化为Cauchy奇异积分方程组与原对偶积分方程组等价性，以及对偶积分方程组解的存在性和唯一性．给出的解法和理论解，作为求解复杂对偶积分方程组一种有效解法，可供求解复杂的数学、物理、力学中的混合边值问题应用．

A Method of Solving a Kind on Dual Integral Equations Via Decoupling Into Canonical Cauchy Singular Integral Equations

Based on method of Mellin transform, the dual integral equations of complex and more general form is solved. The changing equations of real number field into the ones on complex number field by integral transform, the equations are decoupled and reduced into the canonical Cauchy singular integral equations by integral transformation of introduced unknown function, moving the line of integration, using Cauchy integral theorem. Thus a general solutions are given. The equivelence between regular Cauchy singular integral equations on decouple of dual integral equations and original dual integral equations, the existence and uniqueness on solutions are proved exactly. The given theoretical solutions and solving method in this paper are furnished another valid method of solving complex dual integral equations. At the time applications to problem of solving mixed boundary value of complex mathematics, physics, mechanics are provided.