On some singular perturbed system of three equations in partial derivatives of the first order

The asymptotics of solution of a singular perturbed system consisting of three equations with partial derivatives of the first order is build and founded. The small parameter belongs to the system in such a way that non-uniformly scaled operators of the left parts of equations are formed. We use the boundary functions method asymptotics construction and so in particular reduce the system to standard initial problems with partial equations. When we proof the theorem on residual terms estimate we apply an already known scheme blending together a specific principle of maximum and including non-standard terms of the boundary layers part of asymptotics.