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IMA Journal of Applied Mathematics Advance Access originally published online on June 26, 2008
IMA Journal of Applied Mathematics 2009 74(1):35-45; doi:10.1093/imamat/hxn009
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A singular perturbation problem with discontinuous data in a cuboid

José L. López{dagger} and Ester Pérez Sinusía{ddagger}

Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain

{dagger} Email: jl.lopez{at}unavarra.es

{ddagger} Email: ester.perez{at}unavarra.es

Received on September 10, 2007; Revision received September 10, 2007. Accepted on March 3, 2008

We analyse the asymptotic behaviour of the solution of a 3D singularly perturbed convection–diffusion problem with discontinuous Dirichlet boundary data defined in a cuboid. We write the solution in terms of a double series and we obtain an asymptotic approximation of the solution when the singular parameter {epsilon} -> 0. This approximation is given in terms of a finite combination of products of error functions and characterizes the effect of the discontinuities on the small {epsilon}-behaviour of the solution in the singular layers.

Keywords: singular perturbation problem; discontinuous boundary data; asymptotic expansions; error function.


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