In this paper, we discuss the solution of mixed integral equation with generalized potential function in position and the kernel of Volterra integral term in time. The solution will be discussed in the space $$L_{2} (\Omega ) \times C[0,T],$$ $$0 \le t \le T < 1$$ , where $$\Omega$$ is the domain of position and $$t$$ is the time. The mixed integral equation is established from the axisymmetric problems in the theory of elasticity. Many special cases when kernel takes the potential function, Carleman function, the elliptic function and logarithmic function will be established.

中文翻译：

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求解某些域混合积分方程的渐近模型

在本文中，我们讨论了位置上的广义势函数和Volterra积分项时间上的核的混合积分方程的解。该解决方案将在空间 $$L_{2} (\Omega ) \times C[0,T],$$ $$0 \le t \le T < 1$$ 中讨论，其中 $$\Omega$$ 是位置域和 $$t$$ 是时间。混合积分方程是根据弹性理论中的轴对称问题建立的。核取势函数时的许多特殊情况，会建立卡尔曼函数、椭圆函数和对数函数。