Volume 9, Number 2, Summer 2001
ANGULAR LAYER OF A SINGULARLY PERTURBED PARABOLIC PROBLEM WITH CORNER SINGULARITY
SHAGIDI 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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