Asymptotic analysis of singularly perturbed integro-differential equations with zero operator in the differential part (Q647682)

The authors investigate a vector integro-differential equation with identically zero operator in the differential part. They construct a regularized asymptotics of the solution of that equation for two cases. In one of the cases the integral operator contains an exponentially varying factor and in the other case the integral operator does not. On the basis of the resulting asymptotic expansion, the authors study the passage to the limit in the considered vector equation and establish conditions under which that passage is uniform on the entire range of the independent variable, including the boundary layer region.