### 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 language | English |
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Pages (from-to) | 309-318 |

Number of pages | 10 |

Journal | Asymptotic Analysis |

Volume | 38 |

Issue number | 4 |

Publication status | Published - 2004 |

### Keywords

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

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## Cite this

Grasman, J., & Shih, S. D. (2004). A parabolic singular perturbation problem with an internal layer.

*Asymptotic Analysis*,*38*(4), 309-318. http://iospress.metapress.com/openurl.asp?genre=article&issn=0921-7134&volume=38&issue=3&spage=309