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.
|Number of pages||10|
|Publication status||Published - 2004|
- hyperbolic conservation-laws
- weak solutions
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