Dynamical boundary value problem for a viscoelastic half-space with cut

TL;DR

This paper develops a mathematical approach to solve a boundary value problem involving a viscoelastic half-space with a cut, using singular integral equations and orthogonal polynomials.

Contribution

It introduces a novel reduction method for solving the boundary value problem of viscoelastic materials with cuts, including proof of system regularity.

Findings

Reduction of the boundary value problem to a singular integral equation.

Development of an approximate solution method using orthogonal polynomials.

Proof of quasi-complete regularity of the resulting linear system.

Abstract

The dynamical boundary value problem for viscoelastic half-space with cut in the form of a strip is considered. The problem is reduced to the singular integral equation of first kind. Using the method of orthogonal polynomials, the integral equation is reduced to an infinite system of linear algebraic equations. The quasi-completely regularity of the obtained system is proved and the reduction method for approximate solution is developed.