Renormalization group approach to boundary layer problems

Abstract

Renormalization group(RG) method in the singular perturbation theory, originally introduced by Chen et al, has been proved to be very practicable in a large number of singular perturbed problems. In this paper, we firstly reconsider the RG method and give a new formulation of the renormalized procedure. Then we apply our strategy to investigate several kinds of singular perturbed boundary layer problems, our results show that the RG method has the same efficiency as the classical matched asymptotic expansion method, and can be viewed as a preliminary answer to the open problem proposed by Kirkinis.