A Distributional Approach to the Boundary Layer Theory

We present a distributional approach for solving problems in the boundary layer and singular perturbation theories. We discuss the asymptotic expansions in the inner and outer regions and their matching in the overlapping domain by our theory. This technique is illustrated with various examples from the initial value and boundary value problems. From this discussion we find that the distributional approach not only simplifies the analysis but also widens the scope of applications.