Affiliations: Department of Mathematics and Statistics, Memorial University, St. John's, Canada. E-mail: ou@mun.ca | Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Hong Kong, China. E-mail: mawong@cityu.edu.hk
Note: [] Corresponding author: R. Wong, Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China. E-mail: mawong@cityu.edu.hk
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.
Keywords: boundary value problem, multiple scale, singular perturbation
