A parabolic singular perturbation problem with an internal layer

J. Grasman, S.D. Shih

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner layer as otherwise terms in the internal layer solution remain unnoticed. The problem is explained using the exact solution of a special case. The asymptotic solution is proved to approximate the exact solution in the general case using the maximum principle for parabolic differential equations.
Original languageEnglish
Pages (from-to)309-318
Number of pages10
JournalAsymptotic Analysis
Volume38
Issue number4
Publication statusPublished - 2004

Keywords

  • hyperbolic conservation-laws
  • differential-equations
  • boundary-layers
  • weak solutions

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