An asymptotic model for solving mixed integral equation in some domains

Abstract

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 $$L_{2} (\Omega ) \times C[0,T],$$ L 2 ( Ω ) × C [ 0 , T ] , $$0 \le t \le T < 1$$ 0 ≤ t ≤ T < 1 , where $$\Omega$$ Ω is the domain of position and $$t$$ 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.

A new Model for Solving Three Mixed Integral Equations with Continuous and Discontinuous Kernels

“…The MIE of the first kind can be solved analytically using one of the following methods: The Cauchy method, orthogonal polynomial method, potential theory method and Krein's method, see [9][10][11][12][13][14][15][16] and the references therein for details. The relation between the MIEs and some contact problems can be found in [13][14][15][16][17] and the references therein. This work is a new contribution, to the best of our knowledge, in this active area of scientific research.…”