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J. Melenk, C. Xenophontos, L. Oberbroeckling:
"Analytic regularity for a singularly perturbed system of reaction-diffusion equtions with multiple scales: proofs";
in: "ASC Report 29/2011", issued by: Institute of Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

We consider a coupled system of two singularly perturbed reaction-diffusion equations, with
two small parameters 0 < " μ 1, each multiplying the highest derivative in the equations.
The presence of these parameters causes the solution(s) to have boundary layers which overlap
and interact, based on the relative size of " and μ. We construct full asymptotic expansions
together with error bounds that cover the complete range 0 < " μ 1. For the present case
of analytic input data, we derive derivative growth estimates for the terms of the asymptotic
expansion that are explicit in the perturbation parameters and the expansion order.

http://www.asc.tuwien.ac.at/preprint/2011/asc29x2011.pdf