Construction of an asymptotic limit mode in a system of integral equations

Abstract

We study the passage to the limit in a singularly perturbed integral system with a small parameter and a rapidly decaying kernel. In contrast to classical systems with a small parameter, the exact solution of such a system tends to infinity as the small parameter tends to zero, and hence the limit mode must be constructed in a special way. The construction of the limit mode based on the analysis of the asymptotics of the solution of the equivalent regularized (in the sense of S.A. Lomov) integro-differential system requires laborious computations. We suggest an approach to the construction of the limit mode in such systems based on the original data of the system without the construction of the corresponding asymptotic solution and not requiring heavy computations.