Singular perturbation of an exterior Dirichlet problem

This paper discusses a class of singular perturbation problems such as those of slow viscous flow past a cylinder. A semilinear second-order elliptic equation with a small parameter is used as a model to illustrate the correlation between a regular perturbation procedure and the method of matched asymptotic expansions. Some justification of the formal inner and outer expansions is established. It is found that the use of integral equations of the first kind for treating such a class of singular perturbation problems seems most desirable.