A novel generalized solution expansion for the Lagerstrom model

Abstract

In this paper we re-visit the Lagerstrom problem

y" + (n-1)/r y' + εyy' = 0,

y(1) = 0, y(∞) = 1,

where ε is a small positive real number and n is a positive integer (or any real number greater than 2). Using rigorous analysis, a generalized asymptotic expansion, as ε→0, is derived for the solution of this problem. A trans-series expansion of the solution for large values of r is also presented; the leading term coefficient is determined by a connection formula between the values of the solution at the two points r=1 and r=∞. An extension and a discussion of the problem for n∈[1,2) is also given.