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On the asymptotic solution of an elliptic interior layer problem

1976
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The Journal of the Australian Mathematical Society Series B Applied Mathematics
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An interior layer problem posed by an elliptic partial differential equation of the type e V 2 <£ -x3/dy = f(x, y, e ), 0 < e < 1, is investigated. This equation arises, for example, in the theory of rotating fluids and the important feature of the problem is an interior layer of width O(e'") in which the solution has a relatively large magnitude. The paper considers the simplest case which involves an interior layer, that is, where the domain is rectangular and f(x, y, e) = EA for A constant.

doi:10.1017/s0334270000001351
fatcat:w6g5anxu6naptkevgxdxkf3xwi