3rd TAGRA

This paper is devoted to the asymptotic analysis of a system of singularly perturbed integral equations with a piecewise-smooth matrix kernel. The presence of a small parameter multiplying the unknown function leads to a singular perturbation problem, in which the limiting equation may not adequately describe the behavior of the solution. The main objective is to construct an asymptotic approximation of the solution as the perturbation parameter tends to zero. For this purpose, a regularization method based on the Dirac delta function is employed. The proposed approach enables the integral operator to be transformed into a form suitable for systematic asymptotic analysis. Under appropriate smoothness and spectral assumptions on the kernel matrices, an asymptotic representation of the solution is constructed. The results provide a framework for investigating singularly perturbed integral systems with discontinuous kernels and contribute to the development of regularization techniques for nonlocal problems.