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Volume 9,     Number 2,     Summer 2001

 

ANGULAR LAYER OF A SINGULARLY PERTURBED PARABOLIC PROBLEM WITH CORNER SINGULARITY
SHAGI-DI SHIH

Abstract. For a linear singularly perturbed time dependent convection diffusion problem, the solution possesses angular layer behavior if the input data don’t satisfy certain compatibility conditions at the inflow corner. Its angular layer structure is investigated by virtue of a method of matched asymptotic expansions. The magnitudes of the jump discontinuities of the outer solution and its first two derivatives are derived and are then used to construct an angular layer function, which is solved in terms of the first iterated integral of the complementary error function. The asymptotic approximation obtained is shown to be uniformly valid with the first order accuracy in the small parameter by employing the maximum principle and some exponential decay estimate of the angular layer function.

 

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