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Among the numerical methods for solving applied problems of mathematical physics is the method of boundary integral equations, which translates the main difficulties of research and numerical calculations into some boundary integral equations that relate only to the boundary of a given area and directly take into account the boundary conditions of the problem. The application of the method of boundary integral equations makes it possible to immediately determine the unknown quantities at the boundary itself, without calculating them in the whole domain.In this paper, a system of finite-time integral equations of the second kind is obtained for the formulated plane problem. An algorithm for time steps for numerical solution of such a system of boundary integral equations is proposed.

viscoelasticity, relaxation core, Abel model, relaxation function, viscoelastic potential, fundamental solution, potential density, core of integral equation, moving boundary.