Slowly Varying Phase Planes and Boundary-Layer Theory

William L. Kath*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


A method is presented that combines phase-plane techniques with the ideas of multiple scale and matched asymptotic expansions to explain the behavior of solutions to second-order, nonlinear, nonautonomous, singular boundary-value problems. It is shown that if one is willing to give up the detailed information provided by a procedure such as matched asymptotic expansions, then complete qualitative information can be obtained by the much simpler method given here. ("Complete" here means that the method provides a way of categorizing all possible solutions of such problems.) In addition, the similarities and differences between the present method and that of Melnikov, which has been useful in the study of dynamical systems, are noted.

Original languageEnglish (US)
Pages (from-to)221-239
Number of pages19
JournalStudies in Applied Mathematics
Issue number3
StatePublished - Jun 1 1985

ASJC Scopus subject areas

  • Applied Mathematics


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