On a boundary-layer problem

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

20 Scopus Citations
View graph of relations

Author(s)

  • R. Wong
  • Heping Yang

Detail(s)

Original languageEnglish
Pages (from-to)369-398
Journal / PublicationStudies in Applied Mathematics
Volume108
Issue number4
Publication statusPublished - May 2002

Abstract

This is a continuation of our earlier article concerning the boundary-value problem {εy″ + a(x)y′ + b(x) = 0, x ∈ [x -, x +], x - <0 <x +, y(x -) = A, y(x +) = B, where A, B are prescribed constants, and 0 ≤ ε≪ 1 is a small positive parameter. In that article, we assumed the coefficients a(x) and b(x) are sufficiently smooth functions with the behavior given by a(x) ∼ αx and b(x) ∼ β as x → 0, where α > 0 and β/α ≠ 1, 2, 3,.... In the present article, we are concerned with the case α <0 and β/α ≠ 0, -1, -2,.... An asymptotic solution is obtained for the problem, which holds uniformly for all x in [x -, x +]. Our result is proved rigorously, and shows that a previous result in the literature is incorrect.

Citation Format(s)

On a boundary-layer problem. / Wong, R.; Yang, Heping.
In: Studies in Applied Mathematics, Vol. 108, No. 4, 05.2002, p. 369-398.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review